# Imaginary Coefficients

• Nov 4th 2009, 04:19 PM
SHiFT
Imaginary Coefficients
Find a possible polynomial p(x) such that the degree of p(x) is 3 and all of the coefficients are imaginary.
• Nov 4th 2009, 04:33 PM
skeeter
Quote:

Originally Posted by SHiFT
Find a possible polynomial p(x) such that the degree of p(x) is 3 and all of the coefficients are imaginary.

imaginary coefficients? first I've heard of a problem like this.

$p(x) = ix^3 + 2ix^2 + 3ix + 4i = i(x^3 + 2x^2 + 3x + 4)$
• Nov 4th 2009, 04:49 PM
SHiFT
Sorry, I also forgot to include that in the directions it says let p(x) be a polynomial such that p(-1)=0 and p(3)=0
• Nov 5th 2009, 03:29 AM
HallsofIvy
Quote:

Originally Posted by SHiFT
Sorry, I also forgot to include that in the directions it says let p(x) be a polynomial such that p(-1)=0 and p(3)=0

Just a minor detail, right?(Rofl)

Okay that means that x+1 and x- 3 must be factors: write the polynomial as [tex](ax+ b)(x+1)(x-3)= (ax+b)(x^2- 2x+ 1)= ax^3+ (b-2a)x^2+ (a-2b)x+ b[/quote]. Now choose a and b to be imaginary number such that neither b-2a nor a-2b is 0. a= b= i works nicely.