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Math Algebra Beginning Algebra: Early Graphing (4th Edition)

The sign of the discriminant to predict the nature of equation 3 x 2 + 4 x − 7 = 0 . Introduction: The standard expression of the quadratic equation is a x 2 + b x + c = 0 . The value of the disciminant of the quadratic equation is, b 2 − 4 a c If the disciminant is negative number, then the roots of the equation are not real numbers and there is no real solution of the equation. If the discriminant is positive then two condition are possible, If b 2 − 4 a c is a perfect square, the two real number solutions are rational numbers, If b 2 − 4 a c is not a perfect square, the two real number solutions are irrational, If the discriminant is equal to 0 , there is one real number solution to the equation.

The sign of the discriminant to predict the nature of equation 3 x 2 + 4 x − 7 = 0 . Introduction: The standard expression of the quadratic equation is a x 2 + b x + c = 0 . The value of the disciminant of the quadratic equation is, b 2 − 4 a c If the disciminant is negative number, then the roots of the equation are not real numbers and there is no real solution of the equation. If the discriminant is positive then two condition are possible, If b 2 − 4 a c is a perfect square, the two real number solutions are rational numbers, If b 2 − 4 a c is not a perfect square, the two real number solutions are irrational, If the discriminant is equal to 0 , there is one real number solution to the equation.

Beginning Algebra: Early Graphing (4th Edition)

Beginning Algebra: Early Graphing (4th Edition)

4th Edition

ISBN: 9780134178974

Author: John Tobey Jr., Jeffrey Slater, Jamie Blair, Jenny Crawford

Publisher: PEARSON

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Chapter 9.3, Problem 1E

To determine

The sign of the discriminant to predict the nature of equation $3 x^{2} + 4 x - 7 = 0$ .

Introduction: The standard expression of the quadratic equation is $a x^{2} + b x + c = 0$ . The value of the disciminant of the quadratic equation is,

$b^{2} - 4 a c$

If the disciminant is negative number, then the roots of the equation are not real numbers and there is no real solution of the equation.

If the discriminant is positive then two condition are possible,

If $b^{2} - 4 a c$ is a perfect square, the two real number solutions are rational numbers,

If $b^{2} - 4 a c$ is not a perfect square, the two real number solutions are irrational,

If the discriminant is equal to $0$ , there is one real number solution to the equation.

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Chapter 9.2, Problem 4QQ

Chapter 9.3, Problem 2E

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Let 2 A = 4 3 -4 0 1 (a) Show that v = eigenvalue. () is an eigenvector of A and find the corresponding (b) Find the characteristic polynomial of A and factorise it. Hint: the answer to (a) may be useful. (c) Determine all eigenvalues of A and find bases for the corresponding eigenspaces. (d) Find an invertible matrix P and a diagonal matrix D such that P-¹AP = D.

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Chapter 9 Solutions

Beginning Algebra: Early Graphing (4th Edition)

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Prob. 30PFE Ch. 9 - Prob. 31PFE Ch. 9 - Prob. 32PFE Ch. 9 - The area of a triangle is 68 square meters.The...

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