Question

If $x=2$ and $x=-3$ are roots of the quadratic equation $a{x}^2+7x+b=0$, find the values of $a$ and $b$.

Answer 1

Given $x=2$ & $x=-3$

are roots of quadratic equation

$a{x}^2+7x+b=0$ ....(1)

for $x=-2$

$4a+14+b=0$

$4a+b=-14$ ....(2)

For $x=-3$

$9q-21+b=0$

$9a+b=21$....(3)

On subtraction eq (2) & (3) we get

$4a+b=-14$

$9a+b=21$

=>$-5a=-35$

$[a=7]$ & $b=21-63=-42$

$[b=-42]$