SOLUTION: the difference between the roots of x^2 - 7x - 9 = 0 is a) 7 b) 7/2 c) 9 d) 2 square root 85 e) square root 85

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Question 233404: the difference between the roots of x^2 - 7x - 9 = 0 is
a) 7 b) 7/2 c) 9 d) 2 square root 85 e) square root 85
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
For ax%5E2+%2B+bx+%2Bc+=+0 the roots are:
x+=+%28-b+%2B+sqrt%28b%5E2+-+4ac%29%29%2F%282a%29
and
x+=+%28-b+-+sqrt%28b%5E2+-+4ac%29%29%2F%282a%29
The difference would be:
%28-b+%2B+sqrt%28b%5E2+-+4ac%29%29%2F%282a%29+-+%28-b+-+sqrt%28b%5E2+-+4ac%29%29%2F%282a%29
These two fractions have the same denominator so we can go ahead and subtract. The -b's in the numerator cancel and we end up with:
%282sqrt%28b%5E2-4ac%29%29%2F%282a%29
The 2's cancel leaving:
sqrt%28b%5E2-4ac%29%2Fa

Using this on your equation we get a difference of:

So (e) is the answer.