SOLUTION: The equation x^2+ax+b=0, where a and b are different, has solutions x=a, x=b. How many such equations are there?

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Question 1178355: The equation x^2+ax+b=0, where a and b are different, has solutions x=a, x=b.
How many such equations are there?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


In the equation x%5E2%2Bax%2Bb=0, the sum of the roots is -a and the product of the roots is b.

Then, since the roots are a and b...

(1) a+b=-a
(2) ab = b

Equation (2) tells us a=1; then equation (1) tells us 1+b=-1 so b=-2.

ANSWER: There is only one such equation:

x%5E2%2Bx-2=0 which has roots 1 and -2.