Question

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

Answer 1

If $x=\frac{2}{3},x=-3$ are roots, then the eqn will be
$(x-\frac{2}{3})(x-(-3)=0$
$\Rightarrow$ (x- $\frac{2}{3})${(x+3)} = 0
$\Rightarrow$ $x^2$ - $\frac{2}{3}$ x + 3x - 2= 0
⇒ 3$x^2$ -2x+9x-6=0
⇒ 3$x^2$ +7x-6=0 is the required eqn.

Compare the eqn with ax²+7x+b=0

We have $a=3,$ and $b=-6$

Hence, $a=3,$ and $b=-6$