Question

Verify whether $1$ and $\frac{3}{2}$ are the roots of the equation $2x^2-5x+3=0$

Answer 1

Let $\alpha ,\beta$ be roots of equation (1) then $\alpha +\beta =\frac{5}{2}$ & $\alpha \beta =\frac{3}{2}$ ________- (2)

Given $\alpha =1$ & $\beta =\frac{3}{2}$

now from equation (2)

$1+\frac{3}{2}=\frac{5}{2}$ & $1\times \frac{3}{2}=\frac{3}{2}$

$[\frac{5}{2}=\frac{5}{2}]$ $[\frac{3}{2}=\frac{3}{2}]$

Hence quien roots satisfies the equation (2)

$\therefore 1,\frac{3}{2}$ are roots of equation (1)