Find a formula for the polynomial P ( x ) with degree 3 real coefficients zeros at x = 1 + 2 i and x = − 2 y -intercept at ( 0 , − 40 )

Question

Find a formula for the polynomial  with

with degree 3 real coefficients

zeros at x = 1 + 2 i and x = − 2

y -intercept at ( 0 , − 40 )

Answer 1

P(x)=K(X+2) [(x-1)+2i][(x-1)-2i]=

K(x-2) [(x-1)^2+4]=

K(x-2) [ x^2 -2x +5]

(0,-40) means k(-2)(5)=-40

Then k=4

Answer: 4(x-2) [ x^2 -2x +5]