112k views
3 votes
HELLP!!!!!!!!

"Write the simplest polynomial function using the three zeros given, where all coefficients are integers and the leading coefficient is positive. Enter your answers below."

HELLP!!!!!!!! "Write the simplest polynomial function using the three zeros given-example-1

2 Answers

4 votes

Answer:


{x}^(3) + 2 {x}^(2) - 34x + 7

Explanation:

Since the zeros are 4,1 and -7

We say


(x - 4)(x - 1)(x + 7)

Are the equations

Expanding this we get


{x}^(3) + 2 {x}^(2) - 34x + 7

User Aung Si Min Htet
by
8.2k points
3 votes

Answer:


\large\text{$f(x)=\boxed{1}\;x^3+\boxed{2}\;x^2+\boxed{-31}\;x+\boxed{28}$}

Explanation:

If x = a is a zero (root) of a polynomial function f(x), then (x - a) is a factor of the polynomial function.

Given zeros:


  • x = 4

  • x = 1

  • x = -7

Therefore, the factors of polynomial f(x) are:


  • (x - 4)

  • (x - 1)

  • (x - (-7))=(x+7)

Multiply these factors together to find the polynomial f(x):


f(x)=(x-4)(x-1)(x+7)


f(x)=(x^2-x-4x+4)(x+7)


f(x)=(x^2-5x+4)(x+7)


f(x)=x^3+7x^2-5x^2-35x+4x+28


f(x)=x^3+2x^2-31x+28

Therefore, the simplest polynomial function with the given zeros is:


\large\text{$f(x)=\boxed{1}\;x^3+\boxed{2}\;x^2+\boxed{-31}\;x+\boxed{28}$}

User Yaniv Kessler
by
8.2k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories