PRE CALCULUS 12 GRADE

Question

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

Answer 1

5th degree

with zeros 0, sqr3, i

imaginary roots come in conjugate pairs, so minus i is also a root

x(x-sqr3)(x+sqr3)(x-i)(x+i)

= a 5th degree polynomial when expanded, multiplied out

= x(x^2 -3)(x^2+1)

= x(x^4 -2x^2 -3)

= x^5 -2x^3 -3x

also any multiple of that such as double each term

2x^5 -4x^3-6x

Answer 2

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

Answer 3

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.