Thread: linear and quadratic polynomials

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.

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)

thanks for checking my answer.