One zero of the polynomial function f (x) = x3 + x2 + 20x is x = 0. What are the zeros of the polynomial function?

0, - 5, - 4

0, - 5, 4

0, 5, - 4

0, 5, 4

The correct option is C

Step-by-step explanation:

if f (x) = x3 + x2 - 20x

Replace f (x) by y

y = x3 + x2 - 20x

0 = x3 + x2 - 20x

x3 + x2 - 20x = 0

Take out x as a common:

x (x2+x-20) = 0

Find factors of x2+x+20.

x (x^2+4x-5x-20) = 0

x{x (x+4) - 5 (x+4) }=0

x (x+4) (x-5) = 0

Set x = 0

x=0, x+4=0, x-5 = 0

x=0, x=0-4, x=0+5

x=0, x = - 4, x=5

x = (0,5,-4)

The correct option is C ...

given polynomial function

f (x) = x³ + x² + 20 x ... (1)

x³ + x² + 20 x = 0

so, to find the zeroes we can use options to get the answer.

As roots will satisfy the equation now what we will do to get the answer is put the value in the polynomial.

At x = 0 f (x) = 0 hence zero will be the one of the zeroes of the problem

At x = 5 f (x) = 5³ + 5² + 20 * 5 = 250 hence 5 will not be the root.

At x = - 5 f (x) = - 5³ + - 5² + 20 * - 5 = - 200 hence - 5 will also not be the root of the polynomial.

hence, we can clearly say that there is no option which will satisfy.

So, the option correct is none of these.