SOLUTION: Determine the values of p for which one root of the equation x2 - 12x + p = 0 (x2 = x squared) is 2 more than the other root. Many thanks. Walker

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Question 238424: Determine the values of p for which one root of the equation
x2 - 12x + p = 0 (x2 = x squared)
is 2 more than the other root.
Many thanks.
Walker
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
The key to this problem is to understand that is some number, call it "r", is a root then (x-r) is a factor. So we are looking for an equation of the form:
%28x+-+r%5B1%5D%29%28x+-+r%5B2%5D%29+-+0
that simplifies to
x%5E2+-12x+%2B+p+=+0
and where r%5B1%5D+=+r%5B2%5D+%2B+2

Fortunately expressions of the form:
x%5E2+%2Bbx+%2B+c are fairly simple to factor. We just look for the factors of "c" that add up to "b". So in your equation we look for a "p" whose factors add up to -12 and whose factors are 2 apart from each other. With some thought and/or trial and error we should be able to find that -5 and -7 are two apart from each other and they add up to -12. Since "p" is the product of these two factors, "p" is (-5)(-7) = 35. The final equation is:
x%5E2+-12x+%2B+35+=+0 whose roots are (-5) and (-7).