Question

If $\alpha$ and $\beta$ are roots of $2x^2-3x-6=0$, then the equation whose roots are ${\alpha }^2+2$ and ${\beta }^2+2$ will be

• A. $4x^2+49x-118=0$
• B. $4x^2-49x-118=0$
• C. $4x^2-49x+118=0$
• D. $4x^2+49x+118=0$

Answer 1

The correct option is C $4x^2-49x+118=0$

$2x^2-3x-6=0$

$\alpha +\beta =\frac{3}{2}$

$\alpha \beta =-3$

Now roots are ${\alpha }^2+2$ and ${\beta }^2+2$

$sum={\alpha }^2+2+{\beta }^2+2$

$=(\alpha +\beta {)}^2-2\alpha \beta +4$

$=\frac{9}{4}+6+4$

$=\frac{49}{4}$

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

$={\alpha }^2{\beta }^2+2({\alpha }^2+{\beta }^2)+4$

$=9+2\times \frac{33}{4}+4=13+\frac{33}{2}=\frac{59}{2}$

Equation

$x^2-\frac{49x}{4}+\frac{59}{2}=0$

$4x^2-49x+118=0$