If roots of the equation x^2+ax-b=0 are 3 and -7, find a and b?

Sep 5, 2017

$a = 4$, $b = 21$ and equation is ${x}^{2} + 4 x - 21 = 0$

Explanation:

In an equation $p {x}^{2} + q x + r = 0$, sum of roots (solutions) is $- \frac{q}{p}$ and product of roots is $\frac{r}{p}$.

Hence in ${x}^{2} + a x - b = 0$, we have

$- \frac{a}{1} = 3 + \left(- 7\right) = - 4$

or $a = 4$

and $- \frac{b}{1} = 3 \times \left(- 7\right) = - 21$

or $b = 21$

and equation is ${x}^{2} + 4 x - 21 = 0$