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????
-----------------
If 5+2sqrt(3)i is a root, so is 5-2sqrt(3)i.
----------------
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
-----------------------
= (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
===========
Cheers,
Stan H.
|
|
|
