Find a cubic function with the given zeros. -2, 3, -3
I actually found an answer for this but would like to make sure I solved it correctly
My answer was f(x)=x^3+x-9. Please let me know if you get the same answer!

Question

Find a cubic function with the given zeros. -2, 3, -3
I actually found an answer for this but would like to make sure I solved it correctly
My answer was f(x)=x^3+x-9. Please let me know if you get the same answer!

amistre64 · Answer

subtract x from each root, and multiply the results

amistre64 · Answer

-2, 3, -3

-2-x, 3-x, -3-x

now when x is any of those values, we get at least one of them to be a zero;  anything times zero is zero

f(x) = (-2-x) (3-x) (-3-x)

amistre64 · Answer

and any constant multiplier of it would work as well, i believe in this case that the "proper" outcome (a positive x^3 term) you might want to multiply it by -1 as well

amistre64 · Answer

we could also test your results ...

 f(x)=x^3+x-9 ; let x = -2

(-2)^3+(-2)-9 ; let x = -2

-8-2-9  does not equal zero .... so it does not have -2 as a root