SOLUTION: The roots of (x-1)(x-2)=p are equal. Find p. The answer is p=1/4, how do they get that?

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Question 1109774: The roots of (x-1)(x-2)=p are equal. Find p.
The answer is p=1/4, how do they get that?
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39838) About Me  (Show Source):
You can put this solution on YOUR website!
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The roots of (x-1)(x-2)=p are equal. Find p.
The answer is p=1/4, how do they get that?
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x%5E2-3x%2B2-p=0

"Equal Roots"
%283-sqrt%289-4%282-p%29%29%29%2F2=%283%2Bsqrt%289-4%282-p%29%29%29%2F2

3-sqrt%289-8%2B4p%29=3%2Bsqrt%289-8%2B4p%29

-sqrt%281%2B4p%29=sqrt%281%2B4p%29

0=2%2Asqrt%281%2B4p%29

sqrt%281%2B4p%29=0, both sides were multiplied by 1%2F2;

square both sides:
1%2B4p=0

4p=-1

highlight_green%28p=-1%2F4%29
?

(Possible mistake of sign somewhere)

Answer by greenestamps(13367) About Me  (Show Source):
You can put this solution on YOUR website!


The answer, as the other tutor showed, is -1/4, not 1/4.

If the roots of %28x-1%29%28x-2%29=p are equal, then %28x-1%29%28x-2%29-p is a perfect square.

%28x-1%29%28x-2%29-p+=+x%5E2-3x%2B2-p

If that is to be a perfect square, then it must be equal to %28x-3%2F2%29%5E2+=+x%5E2-3x%2B9%2F4.

Therefore, 2-p+=+9%2F4 --> p+=+-1%2F4