Question

Find a polynomial of degree 3 w/ real coefficient that satisfies the given conditions. Zeros of 6 & i, P(1)= -10
Please show steps.

Answer 1

well it means the polynomial is

\[P(x) = a(x - 6)(x - i)(x + i)\]

the last 2 linear binomials become

\[x^2 + 1\]

so the polynomial is

\[P(x) = a(x - 6)(x^2 + 1)\]

so from here, just distribute it... and then substitute x = 1 and P(1) = 10
to find the value of a.