Question

What are the zeros of the polynomial function f(x) = x3 + x2 − 20x?

A. 0, −5, −4
B. 0, −5, 4
C. 0, 5, −4
D. 0, 5, 4

Answer 1

`x^3 + x^2 - 20x=0\\ x(x^2+x-20)=0\\ x(x^2+5x-4x-20)=0\\ x(x(x+5)-4(x+5))=0\\ x(x-4)(x+5)=0\\ x=0 \vee x=4 \vee x=-5`

Answer 2

B. 0, −5, 4

Explanation:

Given :

`x^(3) +x^(2) -20x`

Solution:

`x^(3) +x^(2) -20x`

taking x common from the given polynomial

⇒
`x(x^(2) +x-20)=0`

⇒
`x(x(x+5)-4(x+5))=0`

⇒
`x(x+5)(x-4)=0`

⇒ x=0 , x+5=0 , x-4=0

⇒x = 0 , x = -5 , x = 4