Thread: complex conjugate roots

I have the following problem which i hope someone can point me in the right direction of solving:

The equation X^4+40x+39 has 4 roots, if two of the roots are the complex conjugate roots 2+J3 and 2-J3 by a process of long divison and slving a quadratic equation find the other two roots.

The exaple I am given in the book i have gives you the real roots to start with but gives no example of an equation that gives you the imaginary roots. I am looking for somehelp with how to get started on this one.

Any help is apprecciated

Hello,

is a root.
Therefore the polynomial can be factored by

We know that .

So the previous line equals to :



Now, you can try the division process...

Originally Posted by ally79

I have the following problem which i hope someone can point me in the right direction of solving:

The equation X^4+40x+39 has 4 roots, if two of the roots are the complex conjugate roots 2+J3 and 2-J3 by a process of long divison and slving a quadratic equation find the other two roots.

The exaple I am given in the book i have gives you the real roots to start with but gives no example of an equation that gives you the imaginary roots. I am looking for somehelp with how to get started on this one.

Any help is apprecciated

Note: Only one of the roots needed to be given since all coefficients of the quartic are real and so the conjugate root theorem could be used to get the other.