Question

One zero of the polynomial function f(x) = x^3 + x^2 + 20x is x = 0. What are the zeros of the polynomial function?

0, −5, −4
0, −5, 4
0, 5, −4
0, 5, 4

Answer 1

Answer: 0, −5, 4

Explanation:

The given function is

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

One of the zero of the given polynomial function is x=0.

To find other zeroes put f(x)=0

`x^3 + x^2 - 20x=0\\\\\Rightarrow\ x(x^2+x-20)=0\ \ \ [\text{Taking x as common}]`

That is

`x^2+x-20=0` or
`x=0`

if
`x^2+x-20=0`

then
`x^2+5x-4x-20=0\ \ \ [\text{By using middle term splitting method}]`

`\Rightarrow\ x(x+5)-4(x+5)=0\\\\\Rightarrow\ (x+5)(x-4)=0\\\\\Rightarrow\ x=-5, 4`

So, the zeroes of f(x) are 0, −5, 4 .

Hence, the correct option is 0, −5, 4.