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

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- November 4th 2009, 03:19 PMSHiFTImaginary Coefficients
Find a possible polynomial p(x) such that the degree of p(x) is 3 and all of the coefficients are imaginary.

- November 4th 2009, 03:33 PMskeeter
- November 4th 2009, 03:49 PMSHiFT
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

- November 5th 2009, 02:29 AMHallsofIvy
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.