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?

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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?

Mathematics
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Expand:\[(x-2)(x-5-2i)(x-5+2i)\]
Here's the properly formatted equation. \[x ^{3}-12x ^{2}+cx+d=0\]
Hmm, alright. Let me do that. 2 minutes.

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

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