• Sep 1st 2007, 07:53 AM
wayne
Need help with this one please, The degree three polynomial f(x) with real coefficients and leading coefficient 1, has -3 and + 4i among its roots. Express f(x) as a product of linear and quadratic polynomials with real coefficients. my answer is f(x) = (x-3)(x^2-8x+16) thanks for checking. would like to make sure.
• Sep 1st 2007, 07:59 AM
earboth
Quote:

Originally Posted by wayne
Need help with this one please, The degree three polynomial f(x) with real coefficients and leading coefficient 1, has -3 and + 4i among its roots. Express f(x) as a product of linear and quadratic polynomials with real coefficients. my answer is f(x) = (x-3)(x^2-8x+16) thanks for checking. would like to make sure.

Hello,

- if x = -3 is a solution then the corresponding linear factor is (x+3)

- if x = 4i is a solution then x = -4i is a solution too. Otherwise you will get an equation containing imaginary numbers. The linear factors are now (x-4i) and (x+4i).

- f(x) = (x+3)(x-4i)(x+4i) = (x+3)(x^2+16)
• Sep 1st 2007, 08:21 AM
wayne
thank you