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

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.

campbell_st · Answer

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.