Question

If $\alpha$, $\beta$ are roots of the equation $2x^2-5x+3=0$, then ${\alpha }^2\beta +{\beta }^2\alpha$ is equal to?

• A. $15/2$
• B. $-15/4$
• C. $15/4$
• D. $-15/2$

Answer 1

The correct option is C $15/4$

$\Rightarrow$ $\alpha$ and $\beta$ are roots of the equation $2x^2-5x+3=0$.

$\Rightarrow$ Here, $a=2,b=-5,c=3$

$\Rightarrow$ $\alpha +\beta =\frac{-b}{a}=-\frac{-5}{2}=\frac{5}{2}$ ------ ( 1 )

$\Rightarrow$ $\alpha \beta =\frac{c}{a}=\frac{3}{2}$ ---- ( 2 )

Now,

$\Rightarrow$ ${\alpha }^2\beta +{\beta }^2\alpha =\alpha \beta (\alpha +\beta )$

$=\frac{3}{2}\times \frac{5}{2}$ [ From ( 1 ) and ( 2 ) ]

$=\frac{15}{4}$

$\therefore$ ${\alpha }^2\beta +{\beta }^2\alpha =\frac{15}{4}$