Given that 2 and 5 + 2i are the roots of the equation x^3 - 12x^2 + cx + d = 0, find the values of c and d. I know that the three roots are 2, 5+2i, and 5-2i. How do I find the values of c and d?

Question

parthkohli · Answer

Expand:$$(x-2)(x-5-2i)(x-5+2i)$$

anonymous · Answer

Here's the properly formatted equation.
$$x ^{3}-12x ^{2}+cx+d=0$$

anonymous · Answer

Hmm, alright. Let me do that. 2 minutes.

anonymous · Answer

Could you explain why we find the quadratic to find the value of c and d? And why do we multiply it with x-2? (I know that because x=2 we use x-2.) I just don't understand why.

anonymous · Answer

The answer I got:

$$x ^{3}-12x^{2}+47x-54$$

So c is 47 and d is -54