Question

If x=2/3 and x= -3 are the roots of the quadritic equation ax2 +7x +b=0 then find the value of a and b.

Answer 1

$sum \: \: of \: \: roots = \frac{2}{3} - 3 = \frac{ - 7}{3} \\ therefore \: \frac{ - 7}{a} = \frac{ - 7}{3} \\ a = 3 \\ product \: \: of \: \: roots = \frac{2}{3} \times - 3 = - 2 \\ therefore \: \frac{ b}{a} = - 2 \\ b = - 2 \times 3 = - 6$