Question 1178355
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In the equation {{{x^2+ax+b=0}}}, the sum of the roots is -a and the product of the roots is b.<br>
Then, since the roots are a and b...<br>
(1) a+b=-a
(2) ab = b<br>
Equation (2) tells us a=1; then equation (1) tells us 1+b=-1 so b=-2.<br>
ANSWER: There is only one such equation:<br>
{{{x^2+x-2=0}}} which has roots 1 and -2.<br>