Question

2/3, 3/2 are two roots, then the quadratic equation is​

Answer 1

The two roots are

$\alpha = \dfrac 23 , ~ \beta = \dfrac 32$

Now,

$x^2 - (\alpha + \beta)x + \alpha \beta =0\\\\\implies x^2 - \left(\dfrac 23 + \dfrac 32\right)x + \left(\dfrac 23 \right) \left(\dfrac 32 \right) =0\\\\\implies x^2 - \left(\dfrac {13x}{6}\right) + 1=0\\\\\implies 6x^2 -13x +6 =0$