Question

If α and β are the roots of the equation $2x^2-3x+4=0$, then the equation whose roots are ${\alpha }^2$ and ${\beta }^2$ is

• A. $4x^2+7x+16=0$
• B. $4x^2+7x+6=0$
• C. $4x^2+7x+1=0$
• D. $4x^2-7x+16=0$

Answer 1

The correct option is A

$4x^2+7x+16=0$

α + β = $\frac{3}{2}$ and αβ = 2

${\alpha }^2+{\beta }^2=(\alpha +\beta {)}^2-2\alpha \beta =\frac{9}{4}-4=-\frac{7}{4}$

hence required equation $x^2-({\alpha }^2+{\beta }^2)x+{\alpha }^2{\beta }^2=0$

⇒ $x^2+\frac{7}{4}x+4=0$ ⇒ $4x^2+7x+16=0$