Question

For what the value of a and b , x= 3/4 and x=2 are solution of the equation ax^2+bx+6=0

Answer 1

The sum of the roots of the quadratic equation $ax^2+bx+6=0$ is

$-\frac{b}{a}$ and the product of the roots is $\frac{6}{a}$.

Since $3/4,2$ are the roots of the given equation,

$\frac{6}{a} =\frac{3}{4}*2=\frac{3}{2}\\ a=4\\ -\frac{b}{a} = \frac{3}{4}+2=\frac{11}{4}\\ b=-\frac{11}{4}*4\\ b=-11$