SOLUTION: Find the 3rd degree polynomial with real coefficients with -6 and i zeros and f(-3)=60.

Question 611040: Find the 3rd degree polynomial with real coefficients with -6 and i zeros and f(-3)=60.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

If -6 is a zero, then

is a factor of the polynomial.

if

is a zero, then

is also a zero because complex roots always appear in conjugate pairs, i.e.

The product of a pair of conjugates is the difference of two squares, so the product of

So the product

is the family of polynomial functions contained in which is the particular function you are looking for.

Expand the product above and set the whole thing equal to 60. Then substitute -3 for x, leaving you with a single variable equation in

. Solve for

and collect terms to write your specific third degree polynomial.

John

My calculator said it, I believe it, that settles it

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