# Planet Venus

• Dec 21st 2008, 07:53 PM
magentarita
Write A Polynomial Function
Write a polynomial function of least degree that has real coefficients, the given zeros and a leading coefficient of 1.
4, -4, -3i
• Dec 22nd 2008, 06:20 AM
HallsofIvy
Quote:

Originally Posted by magentarita
Write a polynomial function of least degree that has real coefficients, the given zeros and a leading coefficient of 1.
4, -4, -3i

You can solve polynomial equations by factoring right? If p(x)= (x-a)(x-b)(x-c) then x= a, x= b, and x= c are the zeros. And the fact that the coefficient of each x is 1 means that the leading coefficient after you have multiplied it out will be 1. The answer to the problem as you have stated it is (x- 4)(x+ 4)(x+ 3i).

WARNING! You did NOT say that the polynomial must have real coefficients! For example, the constant term of that would be -48i. If you are also required to have real coefficients you will need the "complex conjugate" also as a zero: (x-4)(x+4)(x+ 3i)(x-3i).
• Dec 22nd 2008, 08:58 PM
magentarita
ok..........
Quote:

Originally Posted by HallsofIvy
You can solve polynomial equations by factoring right? If p(x)= (x-a)(x-b)(x-c) then x= a, x= b, and x= c are the zeros. And the fact that the coefficient of each x is 1 means that the leading coefficient after you have multiplied it out will be 1. The answer to the problem as you have stated it is (x- 4)(x+ 4)(x+ 3i).

WARNING! You did NOT say that the polynomial must have real coefficients! For example, the constant term of that would be -48i. If you are also required to have real coefficients you will need the "complex conjugate" also as a zero: (x-4)(x+4)(x+ 3i)(x-3i).

That was easy. Thanks!