SOLUTION: One root of the function y=x^2-10x+k is 5+2isqrt3. What is the value of k?

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Question 126472: One root of the function y=x^2-10x+k is 5+2isqrt3. What is the value of k?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
y=x%5E2-10x%2Bk
One root is +5%2B2i%28sqrt%283%29%29+y=x^2-10x+k is 5+2isqrt3
To find:
What is the value of k?
If one root is known, for that value y=0; so, we will have:

if +5%2B2i%28+sqrt%283%29+%29+, then
plug it in the equation:

0+=+%285+%2B+2i%28+1.73%29+%29%5E2+-10%285%2B2i%28+1.73%29%29+%2B+k


0+=+%2825+%2B+10i%28+1.73%29+%2B+4i%5E2%28+1.73%29%5E2+-50+%2B+20i%28+1.73%29%29+%2B+k
0+=+25+%2B+17.3i%2B+4%28-1%29%28+2.99%29+-50+%2B+34.6i+%2B+k
0+=+25+-50+%2B+51.9i+-11.96+%2B+k
0+=+-25+%2B+51.9i+-11.96+%2B+k
0+=+-36.96+%2B+51.9i+%2B+k

36.96+-+51.9i+=+k

k+=+36.96+-+51.9i+

check:
0+=+%285+%2B+2i%28+1.73%29+%29%5E2+-10%285%2B2i%28+1.73%29%29+%2B+36.96+-+51.9i+
0+=+25+%2B+17.3i%2B+4%28-1%29%28+2.99%29+-50+%2B+34.6i+%2B+36.96+-+51.9i+
0+=+25-50+%2B+36.96+-11.96+%2B+17.3i+%2B+34.6i+-+51.9i+
0+=+11.96+-11.96+%2B+51.9i-+51.9i+
0+=+0%2B+0

0+=+0