what's the equation for h

Question

 is a degree 5 polynomial that passes through the origin, has zeros  and , and . Find the equation for .

Use  for your input. Simplify your answer so that it has only real numbers as coefficients.

Answer 1

Hi Kassandra,

Complex roots occur in conjugate pairs, so if i and 5-i are roots, then -i and 5+i must also be roots.

Once you know all the roots, you can write the polynomial in factored form and then use the condition that h(-1) = -370 to find the leading coefficient.