equation of a polynomial function

Question

Find a degree 3 polynomial with real coefficients having zeros  and  and a lead coefficient of 1. Write  in expanded form. Be sure to write the full equation, including $\mathrm{P(x)=.}$



Answer 1

zeroes are 1, 1-4i and 1+4i

imaginary zeroes come in conjugate pairs

x=1-4i

x-1 = -4i

x^2 -2x + 1 = -16

x^2-2x+1 +16 = 0

x^2-2x+17 is one factor, the other is x-1

P(x) = (x-1)(x^2-2x+17)

P(x) = x^3 -3x^2 -15x + 17

(while "zeros" is the more popular plural form of

"zero," used more often than "zeroes"

either is grammatically correct. However Stephen

Hawking used "zeroes" in his Brief History of Time

book. Hawking as a mathematician and physicist

gave a boost to "zeroes," although "zeros" wins

by a landslide in British use)