Question

Find a cubic function with the given zeros.

6, -3, 5

A) f(x) = x3 - 8x2 + 3x + 90

B) f(x) = x3 - 8x2 - 3x + 90

C) f(x) = x3 + 8x2 - 3x + 90

D) f(x) = x3 - 8x2 - 3x - 90

Answer 1

Becuase we have three zeros of the cubic function, we can say that :
\[f(x)=(x-6)(x+3)(x-5)\]
So, by developing the expression you will get the answer ;)

Answer 2

I know that, But what do I do next?

Answer 3

We have :
\[\Large f(x)=(x-6)(x+3)(x-5)\\
\Large ~~=(x^2+3x-6x-18)(x-5)\\
\Large ~~=(x^2-3x-18)(x-5)\\
\Large~~=x^3-5x^2-3x^2+15x-18x+90\\
\Large~~=x^2-8x^2-3x+90
\]

Answer 4

Thanks much!