SOLUTION: The equation 8x-x^2=k-2 has roots a and b. Find the value of k if the roots differ by 2.

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Question 981899: The equation 8x-x^2=k-2 has roots a and b. Find the value of k if the roots differ by 2.
Answer by mananth(16946) About Me  (Show Source):
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The equation 8x-x^2=k-2 has roots a and b. Find the value of k if the roots differ by 2.
x^2-8x+(k-2) =0
a+b = -(-8)/1 =8
ab = k-2
a-b =2
a+b= 8
a-b= 2
2a=10
a=5
a-b =2
b=3
ab = k-2
5*3 = k-2
15 =k-2
k=17