How do I simplify this imaginary expression on the left?

x2−(6+3i)x+k=0

one solution is 3

I solved for k

which is 9−9i (answer is correct)

But I am having issues factoring and simplifying when we plug in k in the original

x2−(6+3i)x+(9−9i)=0

1 Answer
George C.
Nov 13, 2017

k=9+9i

Explanation:

Given:

x2−(6+3i)x+k=0 with root 3

Putting x=3 into the equation, we get:

0=32−(6+3i)(3)+k

0=9−18−9i+k

0=−9−9i+k

So:

k=9+9i

Our original equation becomes:

x2−(6+3i)x+(9+9i)=0

Note that:

6+3i=3+(3+3i) which is the sum of the roots

9+9i=3(3+3i) which is the product of the roots

Factoring, we have:

x2−(6+3i)x+(9+9i)=(x−3)(x−(3+3i))

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