PRE CALCULUS 12 GRADE

Question

Write a polynomial with real coefficient having 5 degree and zeros (0, square root of 3, -i,)

Answer 1

See the video. It's no problem getting to the final answer.

Answer 2

Key here is that roots are 0,±sqrt(3), ±i

The P(x) can found from the form C(x-r₁)(x-r₂)(x-r₃)(x-r₄)(x-r₅) = 0 c=1 makes the leading term x⁵

So P(x) = x(x²-3)(x²+1) taking advantage (x+a)(x-a) = x²-a²

Multiply it out to get your polynomial.