Find a polynomial P(x) with real coefficients having a degree 6, leading coefficient 4, and zeros 4,0 (multiplicity 3), and 3-3i.

Question

Please help me this is urgent.

Answer 1

6 degree poly

with 4x^6 as highest powered term

zeros = 4, 0, 0, 0, 3-3i and 3+3i

4(x-4)(x^3)(x-3-3i)(x-3+3i)

expand, combine like terms

= 4x^3(x-4)(x^2 -6x + 18)

= 4x^3(x^3 -10x^2+42x-72)

= 4x^6 -40x^5 +168x^4 -288x^3

Answer 2

P(x) = 4(x - 4)x³(x - 3 + 3i)(x - 3 - 3i) = 4x³(x - 4)(x² - 6x + 18)