Imaginary Coefficients

SHiFT · #1 $Old$ November 4th, 2009, 05:19 PM

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

skeeter · #2 $Old$ November 4th, 2009, 05:33 PM

Quote:

Originally Posted by SHiFT $View Post$

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.

how about ...

$p(x) = ix^3 + 2ix^2 + 3ix + 4i = i(x^3 + 2x^2 + 3x + 4)$

SHiFT · #3 $Old$ November 4th, 2009, 05:49 PM

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

HallsofIvy · #4 $Old$ November 5th, 2009, 04:29 AM

Quote:

Originally Posted by SHiFT $View Post$

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?

Okay that means that x+1 and x- 3 must be factors: write the polynomial as [math](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.