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

Question 127200: One root of the function y=x^2-10x+k is 5+2isqrt3. What is the value of k????
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
One root of the function y=x^2-10x+k is 5+2isqrt3. What is the value of k????
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If 5+2sqrt(3)i is a root, so is 5-2sqrt(3)i.
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Then the following product is a factor of the given polynomial:
(x-(5+2sqrt(3)i)(x-(5-2sqrt(3)i)
= ((x-5)-2sqrt(3)i)((x-5)+2sqrt(3)i)
Comment: Notice that the factors are in the form (a-b)(a+b).
So the product is a^2-b^2
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= (x-5)^2 -(2sqr(3)i)^2
= x^2-10x+25+12
= x^2-12x+37
Comparing that to the original polynominal you see that
k = 37
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Cheers,
Stan H.
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