Question

Form the quadratic equation whose roots are:

$\frac{3}{4}$ and $\frac{-2}{3}$

• A. $2x^2-x-6=0$
• B. $12x^2-x-6=0$
• C. $12x^2+x-6=0$
• D. $2x^2+x-6=0$

Answer 1

The correct option is B $12x^2-x-6=0$

The roots of the equation are, $\frac{3}{4}$ and $\frac{-2}{3}$

$(x-\frac{3}{4})(x-\frac{-2}{3})=0$

$(x-\frac{3}{4})(x+\frac{2}{3})=0$

$x^2+\frac{2}{3}x-\frac{3}{4}x+\left(\frac{-2}{3}\right)\left(\frac{3}{4}\right)=0$

$x^2-\frac{x}{12}-\frac{1}{2}=0$

$\therefore 12x^2-x-6=0$