Algebra 2: New York Edition (holt Mcdougal Larson Algebra 2)
Algebra 2: New York Edition (holt Mcdougal Larson Algebra 2)
2nd Edition
ISBN: 9780618912407
Author: MCDOUGAL LITTEL
Publisher: Mcdougal Littel
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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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Chapter 2.7, Problem 10GP
Solution

The possible numbers of positive real zeros, negative real zeros and imaginary zeros of the given function.

It has been determined that the given function has 4 , 2 or 0 positive real zeros, 0 negative real zero and 0 , 2 or 4 imaginary zeros respectively.

Given:

The function, gx=2x4−8x3+6x2−3x+1 .

Concept used:

According to the Descartes’ rule of signs:

The number of positive real zeros of a polynomial function with real coefficients, fx , is equal to the number of changes in sign of the coefficients of fx or is less than this by an even number.

The number of negative real zeros of a polynomial function with real coefficients, fx , is equal to the number of changes in sign of the coefficients of f−x or is less than this by an even number.

The number of imaginary zeros of a polynomial function with real coefficients, fx , is always even.

Calculation:

The given function is gx=2x4−8x3+6x2−3x+1 .

It can be seen that the number of changes in sign of the coefficients of gx is 4 .

This implies that the possible number of positive real zeros are 4 , 2 or 0 .

Put x=−x in the given function to get,

  g−x=2x4+8x3+6x2+3x+1

It can be seen that the number of changes in sign of the coefficients of g−x is 0 .

This implies that the number of negative real zeros is 0 .

The given function is a polynomial of degree 4 .

This implies that the total number of zeros is 4 .

Hence, the possible number of imaginary zeros are 0 , 2 or 4 .

Conclusion:

It has been determined that the given function has 4 , 2 or 0 positive real zeros, 0 negative real zero and 0 , 2 or 4 imaginary zeros respectively.

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Chapter 2.7, Problem 9GP
Next
Chapter 2.7, Problem 11GP

Chapter 2 Solutions

Algebra 2: New York Edition (holt Mcdougal Larson Algebra 2)

Ch. 2.1 - Prob. 1GPCh. 2.1 - Prob. 2GPCh. 2.1 - Prob. 3GPCh. 2.1 - Prob. 4GPCh. 2.1 - Prob. 5GPCh. 2.1 - Prob. 6GPCh. 2.1 - Prob. 7GPCh. 2.1 - Prob. 8GPCh. 2.1 - Prob. 1ECh. 2.1 - Prob. 2E
Ch. 2.1 - Prob. 3ECh. 2.1 - Prob. 4ECh. 2.1 - Prob. 5ECh. 2.1 - Prob. 6ECh. 2.1 - Prob. 7ECh. 2.1 - Prob. 8ECh. 2.1 - Prob. 9ECh. 2.1 - Prob. 10ECh. 2.1 - Prob. 11ECh. 2.1 - Prob. 12ECh. 2.1 - Prob. 13ECh. 2.1 - Prob. 14ECh. 2.1 - Prob. 15ECh. 2.1 - Prob. 16ECh. 2.1 - Prob. 17ECh. 2.1 - Prob. 18ECh. 2.1 - Prob. 19ECh. 2.1 - Prob. 20ECh. 2.1 - Prob. 21ECh. 2.1 - Prob. 22ECh. 2.1 - Prob. 23ECh. 2.1 - Prob. 24ECh. 2.1 - Prob. 25ECh. 2.1 - Prob. 26ECh. 2.1 - Prob. 27ECh. 2.1 - Prob. 28ECh. 2.1 - Prob. 29ECh. 2.1 - Prob. 30ECh. 2.1 - Prob. 31ECh. 2.1 - Prob. 32ECh. 2.1 - Prob. 33ECh. 2.1 - Prob. 34ECh. 2.1 - Prob. 35ECh. 2.1 - Prob. 36ECh. 2.1 - Prob. 37ECh. 2.1 - Prob. 38ECh. 2.1 - Prob. 39ECh. 2.1 - Prob. 40ECh. 2.1 - Prob. 41ECh. 2.1 - Prob. 42ECh. 2.1 - Prob. 43ECh. 2.1 - Prob. 44ECh. 2.1 - Prob. 45ECh. 2.1 - Prob. 46ECh. 2.1 - Prob. 47ECh. 2.1 - Prob. 48ECh. 2.1 - Prob. 49PSCh. 2.1 - Prob. 50PSCh. 2.1 - Prob. 51PSCh. 2.1 - Prob. 52PSCh. 2.1 - Prob. 53PSCh. 2.1 - Prob. 54PSCh. 2.1 - Prob. 1DCCh. 2.1 - Prob. 2DCCh. 2.1 - Prob. 3DCCh. 2.1 - Prob. 4DCCh. 2.1 - Prob. 5DCCh. 2.1 - Prob. 6DCCh. 2.2 - Prob. 1GPCh. 2.2 - Prob. 2GPCh. 2.2 - Prob. 3GPCh. 2.2 - Prob. 4GPCh. 2.2 - Prob. 5GPCh. 2.2 - Prob. 6GPCh. 2.2 - Prob. 7GPCh. 2.2 - Prob. 8GPCh. 2.2 - Prob. 9GPCh. 2.2 - Prob. 10GPCh. 2.2 - Prob. 11GPCh. 2.2 - Prob. 12GPCh. 2.2 - Prob. 1ECh. 2.2 - Prob. 2ECh. 2.2 - Prob. 3ECh. 2.2 - Prob. 4ECh. 2.2 - Prob. 5ECh. 2.2 - Prob. 6ECh. 2.2 - Prob. 7ECh. 2.2 - Prob. 8ECh. 2.2 - Prob. 9ECh. 2.2 - Prob. 10ECh. 2.2 - Prob. 11ECh. 2.2 - Prob. 12ECh. 2.2 - Prob. 13ECh. 2.2 - Prob. 14ECh. 2.2 - Prob. 15ECh. 2.2 - Prob. 16ECh. 2.2 - Prob. 17ECh. 2.2 - Prob. 18ECh. 2.2 - Prob. 19ECh. 2.2 - Prob. 20ECh. 2.2 - Prob. 21ECh. 2.2 - Prob. 22ECh. 2.2 - Prob. 23ECh. 2.2 - Prob. 24ECh. 2.2 - Prob. 25ECh. 2.2 - Prob. 26ECh. 2.2 - Prob. 27ECh. 2.2 - Prob. 28ECh. 2.2 - Prob. 29ECh. 2.2 - Prob. 30ECh. 2.2 - Prob. 31ECh. 2.2 - Prob. 32ECh. 2.2 - Prob. 33ECh. 2.2 - Prob. 34ECh. 2.2 - Prob. 35ECh. 2.2 - Prob. 36ECh. 2.2 - Prob. 37ECh. 2.2 - Prob. 38ECh. 2.2 - Prob. 39ECh. 2.2 - Prob. 40ECh. 2.2 - Prob. 41ECh. 2.2 - Prob. 42ECh. 2.2 - Prob. 43ECh. 2.2 - Prob. 44ECh. 2.2 - Prob. 45ECh. 2.2 - Prob. 46ECh. 2.2 - Prob. 47ECh. 2.2 - Prob. 48ECh. 2.2 - Prob. 49ECh. 2.2 - Prob. 50ECh. 2.2 - Prob. 51ECh. 2.2 - Prob. 52ECh. 2.2 - Prob. 53ECh. 2.2 - Prob. 54PSCh. 2.2 - Prob. 55PSCh. 2.2 - Prob. 56PSCh. 2.2 - Prob. 57PSCh. 2.2 - Prob. 58PSCh. 2.2 - Prob. 59PSCh. 2.2 - Prob. 60PSCh. 2.2 - Prob. 1PCh. 2.2 - Prob. 2PCh. 2.2 - Prob. 3PCh. 2.2 - Prob. 4PCh. 2.2 - Prob. 5PCh. 2.2 - Prob. 6PCh. 2.2 - Prob. 7PCh. 2.2 - Prob. 8PCh. 2.2 - Prob. 9PCh. 2.2 - Prob. 10PCh. 2.3 - Prob. 1GPCh. 2.3 - Prob. 2GPCh. 2.3 - Prob. 3GPCh. 2.3 - Prob. 4GPCh. 2.3 - Prob. 5GPCh. 2.3 - Prob. 6GPCh. 2.3 - Prob. 1ECh. 2.3 - Prob. 2ECh. 2.3 - Prob. 3ECh. 2.3 - Prob. 4ECh. 2.3 - Prob. 5ECh. 2.3 - Prob. 6ECh. 2.3 - Prob. 7ECh. 2.3 - Prob. 8ECh. 2.3 - Prob. 9ECh. 2.3 - Prob. 10ECh. 2.3 - Prob. 11ECh. 2.3 - Prob. 12ECh. 2.3 - Prob. 13ECh. 2.3 - Prob. 14ECh. 2.3 - Prob. 15ECh. 2.3 - Prob. 16ECh. 2.3 - Prob. 17ECh. 2.3 - Prob. 18ECh. 2.3 - Prob. 19ECh. 2.3 - Prob. 20ECh. 2.3 - Prob. 21ECh. 2.3 - Prob. 22ECh. 2.3 - Prob. 23ECh. 2.3 - Prob. 24ECh. 2.3 - Prob. 25ECh. 2.3 - Prob. 26ECh. 2.3 - Prob. 27ECh. 2.3 - Prob. 28ECh. 2.3 - Prob. 29ECh. 2.3 - Prob. 30ECh. 2.3 - Prob. 31ECh. 2.3 - Prob. 32ECh. 2.3 - Prob. 33ECh. 2.3 - Prob. 34ECh. 2.3 - Prob. 35ECh. 2.3 - Prob. 36ECh. 2.3 - Prob. 37ECh. 2.3 - Prob. 38ECh. 2.3 - Prob. 39ECh. 2.3 - Prob. 40ECh. 2.3 - Prob. 41ECh. 2.3 - Prob. 42ECh. 2.3 - Prob. 43ECh. 2.3 - Prob. 44ECh. 2.3 - Prob. 45ECh. 2.3 - Prob. 46ECh. 2.3 - Prob. 47ECh. 2.3 - Prob. 48ECh. 2.3 - Prob. 49ECh. 2.3 - Prob. 50ECh. 2.3 - Prob. 51ECh. 2.3 - Prob. 52ECh. 2.3 - Prob. 53ECh. 2.3 - Prob. 54ECh. 2.3 - Prob. 55ECh. 2.3 - Prob. 56ECh. 2.3 - Prob. 57ECh. 2.3 - Prob. 58ECh. 2.3 - Prob. 59PSCh. 2.3 - Prob. 60PSCh. 2.3 - Prob. 61PSCh. 2.3 - Prob. 62PSCh. 2.3 - Prob. 63PSCh. 2.3 - Prob. 64PSCh. 2.3 - Prob. 1QCh. 2.3 - Prob. 2QCh. 2.3 - Prob. 3QCh. 2.3 - Prob. 4QCh. 2.3 - Prob. 5QCh. 2.3 - Prob. 6QCh. 2.3 - Prob. 7QCh. 2.3 - Prob. 8QCh. 2.3 - Prob. 9QCh. 2.3 - Prob. 10QCh. 2.3 - Prob. 11QCh. 2.3 - Prob. 12QCh. 2.3 - Prob. 13QCh. 2.3 - Prob. 14QCh. 2.3 - Prob. 15QCh. 2.3 - Prob. 16QCh. 2.4 - Prob. 1GPCh. 2.4 - Prob. 2GPCh. 2.4 - Prob. 3GPCh. 2.4 - Prob. 4GPCh. 2.4 - Prob. 5GPCh. 2.4 - Prob. 6GPCh. 2.4 - Prob. 7GPCh. 2.4 - Prob. 8GPCh. 2.4 - Prob. 9GPCh. 2.4 - Prob. 10GPCh. 2.4 - Prob. 11GPCh. 2.4 - Prob. 1ECh. 2.4 - Prob. 2ECh. 2.4 - Prob. 3ECh. 2.4 - Prob. 4ECh. 2.4 - Prob. 5ECh. 2.4 - Prob. 6ECh. 2.4 - Prob. 7ECh. 2.4 - Prob. 8ECh. 2.4 - Prob. 9ECh. 2.4 - Prob. 10ECh. 2.4 - Prob. 11ECh. 2.4 - Prob. 12ECh. 2.4 - Prob. 13ECh. 2.4 - Prob. 14ECh. 2.4 - Prob. 15ECh. 2.4 - Prob. 16ECh. 2.4 - Prob. 17ECh. 2.4 - Prob. 18ECh. 2.4 - Prob. 19ECh. 2.4 - Prob. 20ECh. 2.4 - Prob. 21ECh. 2.4 - Prob. 22ECh. 2.4 - Prob. 23ECh. 2.4 - Prob. 24ECh. 2.4 - Prob. 25ECh. 2.4 - Prob. 26ECh. 2.4 - Prob. 27ECh. 2.4 - Prob. 28ECh. 2.4 - Prob. 29ECh. 2.4 - Prob. 30ECh. 2.4 - Prob. 31ECh. 2.4 - Prob. 32ECh. 2.4 - Prob. 33ECh. 2.4 - Prob. 34ECh. 2.4 - Prob. 35ECh. 2.4 - Prob. 36ECh. 2.4 - Prob. 37ECh. 2.4 - Prob. 38ECh. 2.4 - Prob. 39ECh. 2.4 - Prob. 40ECh. 2.4 - Prob. 41ECh. 2.4 - Prob. 42ECh. 2.4 - Prob. 43ECh. 2.4 - Prob. 44ECh. 2.4 - Prob. 45ECh. 2.4 - Prob. 46ECh. 2.4 - Prob. 47ECh. 2.4 - Prob. 48ECh. 2.4 - Prob. 49ECh. 2.4 - Prob. 50ECh. 2.4 - Prob. 51ECh. 2.4 - Prob. 52ECh. 2.4 - Prob. 53ECh. 2.4 - Prob. 54ECh. 2.4 - Prob. 55ECh. 2.4 - Prob. 56ECh. 2.4 - Prob. 57ECh. 2.4 - Prob. 58PSCh. 2.4 - Prob. 59PSCh. 2.4 - Prob. 60PSCh. 2.4 - Prob. 61PSCh. 2.4 - Prob. 62PSCh. 2.4 - Prob. 63PSCh. 2.4 - Prob. 64PSCh. 2.4 - Prob. 65PSCh. 2.4 - Prob. 1PCh. 2.4 - Prob. 2PCh. 2.4 - Prob. 3PCh. 2.4 - Prob. 4PCh. 2.4 - Prob. 5PCh. 2.4 - Prob. 6PCh. 2.4 - Prob. 7PCh. 2.4 - Prob. 8PCh. 2.4 - Prob. 9PCh. 2.4 - Prob. 10PCh. 2.5 - Prob. 1GPCh. 2.5 - Prob. 2GPCh. 2.5 - Prob. 3GPCh. 2.5 - Prob. 4GPCh. 2.5 - Prob. 5GPCh. 2.5 - Prob. 6GPCh. 2.5 - Prob. 7GPCh. 2.5 - Prob. 8GPCh. 2.5 - Prob. 9GPCh. 2.5 - Prob. 1ECh. 2.5 - Prob. 2ECh. 2.5 - Prob. 3ECh. 2.5 - Prob. 4ECh. 2.5 - Prob. 5ECh. 2.5 - Prob. 6ECh. 2.5 - Prob. 7ECh. 2.5 - Prob. 8ECh. 2.5 - Prob. 9ECh. 2.5 - Prob. 10ECh. 2.5 - Prob. 11ECh. 2.5 - Prob. 12ECh. 2.5 - Prob. 13ECh. 2.5 - Prob. 14ECh. 2.5 - Prob. 15ECh. 2.5 - Prob. 16ECh. 2.5 - Prob. 17ECh. 2.5 - Prob. 18ECh. 2.5 - Prob. 19ECh. 2.5 - Prob. 20ECh. 2.5 - Prob. 21ECh. 2.5 - Prob. 22ECh. 2.5 - Prob. 23ECh. 2.5 - Prob. 24ECh. 2.5 - Prob. 25ECh. 2.5 - Prob. 26ECh. 2.5 - Prob. 27ECh. 2.5 - Prob. 28ECh. 2.5 - Prob. 29ECh. 2.5 - Prob. 30ECh. 2.5 - Prob. 31ECh. 2.5 - Prob. 32ECh. 2.5 - Prob. 33ECh. 2.5 - Prob. 34ECh. 2.5 - Prob. 35ECh. 2.5 - Prob. 36ECh. 2.5 - Prob. 37ECh. 2.5 - Prob. 38ECh. 2.5 - Prob. 39ECh. 2.5 - Prob. 40ECh. 2.5 - Prob. 41PSCh. 2.5 - Prob. 42PSCh. 2.5 - Prob. 43PSCh. 2.5 - Prob. 44PSCh. 2.5 - Prob. 45PSCh. 2.5 - Prob. 46PSCh. 2.5 - Prob. 1MRPSCh. 2.5 - Prob. 2MRPSCh. 2.5 - Prob. 3MRPSCh. 2.5 - Prob. 4MRPSCh. 2.5 - Prob. 5MRPSCh. 2.5 - Prob. 6MRPSCh. 2.5 - Prob. 7MRPSCh. 2.6 - Prob. 1GPCh. 2.6 - Prob. 2GPCh. 2.6 - Prob. 3GPCh. 2.6 - Prob. 4GPCh. 2.6 - Prob. 5GPCh. 2.6 - Prob. 6GPCh. 2.6 - Prob. 7GPCh. 2.6 - Prob. 1ECh. 2.6 - Prob. 2ECh. 2.6 - Prob. 3ECh. 2.6 - Prob. 4ECh. 2.6 - Prob. 5ECh. 2.6 - Prob. 6ECh. 2.6 - Prob. 7ECh. 2.6 - Prob. 8ECh. 2.6 - Prob. 9ECh. 2.6 - Prob. 10ECh. 2.6 - Prob. 11ECh. 2.6 - Prob. 12ECh. 2.6 - Prob. 13ECh. 2.6 - Prob. 14ECh. 2.6 - Prob. 15ECh. 2.6 - Prob. 16ECh. 2.6 - Prob. 17ECh. 2.6 - Prob. 18ECh. 2.6 - Prob. 19ECh. 2.6 - Prob. 20ECh. 2.6 - Prob. 21ECh. 2.6 - Prob. 22ECh. 2.6 - Prob. 23ECh. 2.6 - Prob. 24ECh. 2.6 - Prob. 25ECh. 2.6 - Prob. 26ECh. 2.6 - Prob. 27ECh. 2.6 - Prob. 28ECh. 2.6 - Prob. 29ECh. 2.6 - Prob. 30ECh. 2.6 - Prob. 31ECh. 2.6 - Prob. 32ECh. 2.6 - Prob. 33ECh. 2.6 - Prob. 34ECh. 2.6 - Prob. 35ECh. 2.6 - Prob. 36ECh. 2.6 - Prob. 37ECh. 2.6 - Prob. 38ECh. 2.6 - Prob. 39ECh. 2.6 - Prob. 40ECh. 2.6 - Prob. 41ECh. 2.6 - Prob. 42ECh. 2.6 - Prob. 43ECh. 2.6 - Prob. 44ECh. 2.6 - Prob. 45PSCh. 2.6 - Prob. 46PSCh. 2.6 - Prob. 47PSCh. 2.6 - Prob. 48PSCh. 2.6 - Prob. 49PSCh. 2.6 - Prob. 50PSCh. 2.6 - Prob. 51PSCh. 2.6 - Prob. 1QCh. 2.6 - Prob. 2QCh. 2.6 - Prob. 3QCh. 2.6 - Prob. 4QCh. 2.6 - Prob. 5QCh. 2.6 - Prob. 6QCh. 2.6 - Prob. 7QCh. 2.6 - Prob. 8QCh. 2.6 - Prob. 9QCh. 2.6 - Prob. 10QCh. 2.6 - Prob. 11QCh. 2.6 - Prob. 12QCh. 2.6 - Prob. 13QCh. 2.6 - Prob. 1PCh. 2.6 - Prob. 2PCh. 2.6 - Prob. 3PCh. 2.6 - Prob. 4PCh. 2.7 - Prob. 1GPCh. 2.7 - Prob. 2GPCh. 2.7 - Prob. 3GPCh. 2.7 - Prob. 4GPCh. 2.7 - Prob. 5GPCh. 2.7 - Prob. 6GPCh. 2.7 - Prob. 7GPCh. 2.7 - Prob. 8GPCh. 2.7 - Prob. 9GPCh. 2.7 - Prob. 10GPCh. 2.7 - Prob. 11GPCh. 2.7 - Prob. 12GPCh. 2.7 - Prob. 1ECh. 2.7 - Prob. 2ECh. 2.7 - Prob. 3ECh. 2.7 - Prob. 4ECh. 2.7 - Prob. 5ECh. 2.7 - Prob. 6ECh. 2.7 - Prob. 7ECh. 2.7 - Prob. 8ECh. 2.7 - Prob. 9ECh. 2.7 - Prob. 10ECh. 2.7 - Prob. 11ECh. 2.7 - Prob. 12ECh. 2.7 - Prob. 13ECh. 2.7 - Prob. 14ECh. 2.7 - Prob. 15ECh. 2.7 - Prob. 16ECh. 2.7 - Prob. 17ECh. 2.7 - Prob. 18ECh. 2.7 - Prob. 19ECh. 2.7 - Prob. 20ECh. 2.7 - Prob. 21ECh. 2.7 - Prob. 22ECh. 2.7 - Prob. 23ECh. 2.7 - Prob. 24ECh. 2.7 - Prob. 25ECh. 2.7 - Prob. 26ECh. 2.7 - Prob. 27ECh. 2.7 - Prob. 28ECh. 2.7 - Prob. 29ECh. 2.7 - Prob. 30ECh. 2.7 - Prob. 31ECh. 2.7 - Prob. 32ECh. 2.7 - Prob. 33ECh. 2.7 - Prob. 34ECh. 2.7 - Prob. 35ECh. 2.7 - Prob. 36ECh. 2.7 - Prob. 37ECh. 2.7 - Prob. 38ECh. 2.7 - Prob. 39ECh. 2.7 - Prob. 40ECh. 2.7 - Prob. 41ECh. 2.7 - Prob. 42ECh. 2.7 - Prob. 43ECh. 2.7 - Prob. 44ECh. 2.7 - Prob. 45ECh. 2.7 - Prob. 46ECh. 2.7 - Prob. 47ECh. 2.7 - Prob. 48ECh. 2.7 - Prob. 49ECh. 2.7 - Prob. 50ECh. 2.7 - Prob. 51ECh. 2.7 - Prob. 52ECh. 2.7 - Prob. 53ECh. 2.7 - Prob. 54ECh. 2.7 - Prob. 55ECh. 2.7 - Prob. 56ECh. 2.7 - Prob. 57ECh. 2.7 - Prob. 58ECh. 2.7 - Prob. 59PSCh. 2.7 - Prob. 60PSCh. 2.7 - Prob. 61PSCh. 2.7 - Prob. 62PSCh. 2.7 - Prob. 63PSCh. 2.7 - Prob. 64PSCh. 2.7 - Prob. 65PSCh. 2.8 - Prob. 1GPCh. 2.8 - Prob. 2GPCh. 2.8 - Prob. 3GPCh. 2.8 - Prob. 4GPCh. 2.8 - Prob. 5GPCh. 2.8 - Prob. 1ECh. 2.8 - Prob. 2ECh. 2.8 - Prob. 3ECh. 2.8 - Prob. 4ECh. 2.8 - Prob. 5ECh. 2.8 - Prob. 6ECh. 2.8 - Prob. 7ECh. 2.8 - Prob. 8ECh. 2.8 - Prob. 9ECh. 2.8 - Prob. 10ECh. 2.8 - Prob. 11ECh. 2.8 - Prob. 12ECh. 2.8 - Prob. 13ECh. 2.8 - Prob. 14ECh. 2.8 - Prob. 15ECh. 2.8 - Prob. 16ECh. 2.8 - Prob. 17ECh. 2.8 - Prob. 18ECh. 2.8 - Prob. 19ECh. 2.8 - Prob. 20ECh. 2.8 - Prob. 21ECh. 2.8 - Prob. 22ECh. 2.8 - Prob. 23ECh. 2.8 - Prob. 24ECh. 2.8 - Prob. 25ECh. 2.8 - Prob. 26ECh. 2.8 - Prob. 27ECh. 2.8 - Prob. 28ECh. 2.8 - Prob. 29ECh. 2.8 - Prob. 30ECh. 2.8 - Prob. 31ECh. 2.8 - Prob. 32ECh. 2.8 - Prob. 33ECh. 2.8 - Prob. 34ECh. 2.8 - Prob. 35ECh. 2.8 - Prob. 36ECh. 2.8 - Prob. 37ECh. 2.8 - Prob. 38ECh. 2.8 - Prob. 39PSCh. 2.8 - Prob. 40PSCh. 2.8 - Prob. 41PSCh. 2.8 - Prob. 42PSCh. 2.8 - Prob. 43PSCh. 2.8 - Prob. 44PSCh. 2.8 - Prob. 1QCh. 2.8 - Prob. 2QCh. 2.8 - Prob. 3QCh. 2.8 - Prob. 4QCh. 2.8 - Prob. 5QCh. 2.8 - Prob. 6QCh. 2.8 - Prob. 7QCh. 2.8 - Prob. 8QCh. 2.8 - Prob. 9QCh. 2.8 - Prob. 10QCh. 2.8 - Prob. 1MRPSCh. 2.8 - Prob. 2MRPSCh. 2.8 - Prob. 3MRPSCh. 2.8 - Prob. 4MRPSCh. 2.8 - Prob. 5MRPSCh. 2.8 - Prob. 6MRPSCh. 2.8 - Prob. 7MRPSCh. 2 - Prob. 1VECh. 2 - Prob. 2VECh. 2 - Prob. 3VECh. 2 - Prob. 4VECh. 2 - Prob. 5REAECh. 2 - Prob. 6REAECh. 2 - Prob. 7REAECh. 2 - Prob. 8REAECh. 2 - Prob. 9REAECh. 2 - Prob. 10REAECh. 2 - Prob. 11REAECh. 2 - Prob. 12REAECh. 2 - Prob. 13REAECh. 2 - Prob. 14REAECh. 2 - Prob. 15REAECh. 2 - Prob. 16REAECh. 2 - Prob. 17REAECh. 2 - Prob. 18REAECh. 2 - Prob. 19REAECh. 2 - Prob. 20REAECh. 2 - Prob. 21REAECh. 2 - Prob. 22REAECh. 2 - Prob. 23REAECh. 2 - Prob. 24REAECh. 2 - Prob. 25REAECh. 2 - Prob. 26REAECh. 2 - Prob. 27REAECh. 2 - Prob. 28REAECh. 2 - Prob. 29REAECh. 2 - Prob. 30REAECh. 2 - Prob. 31REAECh. 2 - Prob. 32REAECh. 2 - Prob. 33REAECh. 2 - Prob. 34REAECh. 2 - Prob. 35REAECh. 2 - Prob. 36REAECh. 2 - Prob. 37REAECh. 2 - Prob. 38REAECh. 2 - Prob. 39REAECh. 2 - Prob. 40REAECh. 2 - Prob. 1TCh. 2 - Prob. 2TCh. 2 - Prob. 3TCh. 2 - Prob. 4TCh. 2 - Prob. 5TCh. 2 - Prob. 6TCh. 2 - Prob. 7TCh. 2 - Prob. 8TCh. 2 - Prob. 9TCh. 2 - Prob. 10TCh. 2 - Prob. 11TCh. 2 - Prob. 12TCh. 2 - Prob. 13TCh. 2 - Prob. 14TCh. 2 - Prob. 15TCh. 2 - Prob. 16TCh. 2 - Prob. 17TCh. 2 - Prob. 18TCh. 2 - Prob. 19TCh. 2 - Prob. 20TCh. 2 - Prob. 21TCh. 2 - Prob. 22TCh. 2 - Prob. 23TCh. 2 - Prob. 24TCh. 2 - Prob. 25TCh. 2 - Prob. 26TCh. 2 - Prob. 27TCh. 2 - Prob. 28TCh. 2 - Prob. 29TCh. 2 - Prob. 1PCh. 2 - Prob. 2PCh. 2 - Prob. 1TPCh. 2 - Prob. 2TPCh. 2 - Prob. 3TPCh. 2 - Prob. 4TPCh. 2 - Prob. 5TPCh. 2 - Prob. 6TPCh. 2 - Prob. 7TPCh. 2 - Prob. 8TPCh. 2 - Prob. 9TPCh. 2 - Prob. 10TPCh. 2 - Prob. 11TPCh. 2 - Prob. 12TPCh. 2 - Prob. 13TPCh. 2 - Prob. 14TPCh. 2 - Prob. 15TPCh. 2 - Prob. 16TPCh. 2 - Prob. 17TPCh. 2 - Prob. 18TPCh. 2 - Prob. 19TPCh. 2 - Prob. 20TPCh. 2 - Prob. 21TP
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