Given that f(x) is a cubic function with zeros at -7 and 4i+3, find an equation for f(x) given that f(-3)=-4

Question

Please provide an answer!!

Answer 1

I prefer to give a METHOD and you can apply it to get the answer.

 

The three zeros are -7 and 3±4i

 

f(x) = a(x-zero)(x-zero)(x-zero)  where each "zero" is a different one of the roots (a.k.a. zeros) of the polynomial f.

 

This requires multiplying out, to begin with, (x-3-4i)(x-3+4i) in your specific case, to get a quadratic factor.

Then that result must be multiplied by (x+7).

 

Lastly, substitute -3 for x and set this whole mess to -4; this enables you to determine what leading coefficient "a" is.