Algebra 2: New York Edition (holt Mcdougal Larson Algebra 2)
2nd Edition
ISBN: 9780618912407
Author: MCDOUGAL LITTEL
Publisher: Mcdougal Littel
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Expert Solution & Answer
Chapter 2, Problem 19T
Solution
To write: A polynomial function f of least degree that has rational coefficients, a leading coefficient of 1 and the given zeros.
The required polynomial function f would be f(x)=x3−6x2+5x+12 .
Given information:
Zeros of a function: −1, 3, 4 .
Formula used:
If x=a, b, c are zeros of the function f(x) , then (x−a), (x−b) and (x−c) would be factors of the function.
Calculation:
For the given problem, there are 3 zeros. This means there will be 3 factors of the given function as:
f(x)=(x−(−1))(x−3)(x−4)=(x+1)(x−3)(x−4)
Now expand the factors using the distributive property (a+b)(c+d)=a⋅c+a⋅d+b⋅c+b⋅d:
f(x)=(x+1)(x−3)(x−4)=(x(x−3)+1(x−3))(x−4)=(x2−3x+x−3)(x−4)=(x2−2x−3)(x−4)=x(x2−2x−3)−4(x2−2x−3)=x3−2x2−3x−4x2+8x+12=x3−6x2+5x+12
Therefore, the required function would be f(x)=x3−6x2+5x+12 .
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
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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 - 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- Problem #3 Let P(G|Q) = 0.03, P(G) = 0.2, and P(Q) = 0.5. a). Find P(GnQ). b). Find P(G UQ). c). Are events G and Q independent or dependent? Explain your reasoning.arrow_forwardProblem #4 Suppose a random variable, X, has the following probability distribution table. X 1 2 3 4 5 60 P(X=x) 0.29 0.11 0.32 0.18 a). Find P(X = 5). b). Find P(2≤ X ≤4). c). Find P(2arrow_forwardProblem #5 You play a game where you have a 35% chance of winning and a 65% chance of losing (no ties are permitted). If you play the game multiple times in a row, the probability of winning and losing remains the same for each attempt. a). If you play the game 40 times, what is the probability that you lose all of the 40 games? b). If you play the game 40 times, what is the probability that you win exactly 25 times?arrow_forward
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- When Hugo is serving at a restaurant, there is a .03 probability that each party will request a high chair for a young child. During one hour, Hugo served 10 parties. Assuming that each party is equally likely to request a high chair, what is the probability that at least one party will request a high chair?Round your answer to the nearest hundredth.arrow_forwardWhen Hiroto is writing, there is \[0.92\]probability that there will be no spelling mistakes on a page. One day, Hiroto writes an essay that is \[11\] pages long. Assuming that Hiroto is equally likely to have a spelling mistake on each of the \[11\] pages, what is the probability that he will have a spelling mistake on at least one of the pages?Round your answer to the nearest tenth.arrow_forwardWhen a customer places an order at Derin's bakery, there is an 85% probability that the order will include some kind of dessert. One day, 7 customers place orders at Derin's bakery. Assuming that each order is equally likely to include dessert, what is the probability that at least one order will not include dessert? Round your answer to the nearest hundredth. P(at least one without dessert) =arrow_forward
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