Question

The equation whose roots are the squares of the roots of the equation $2x^2+3x+1=0$ is

• A. $4x^2+5x+1=0$
• B. $4x^2-x+1=0$
• C. $4x^2-5x-1=0$
• D. $4x^2-5x+1=0$
• E. $4x^2+5x-1=0$

Answer 1

Answer: (D)

$4x^2-5x+1=0$

Given quadratic equation: $2x^2+3x+1=0$

Let $\alpha$ and $\beta$ be two roots

Then, $\alpha +\beta =-\frac{3}{2}$ and $\alpha \beta =\frac{1}{2}$

Now, ${\alpha }^2+{\beta }^2=(\alpha +\beta {)}^2-2\alpha \beta =\frac{9}{4}-1=\frac{5}{4}$

$\Rightarrow {\alpha }^2{\beta }^2=\frac{1}{4}$

Required quadratic equation whose roots are square of roots of above equation$=x^2-({\alpha }^2+{\beta }^2)x+{\alpha }^2{\beta }^2$

$\Rightarrow x^2-\frac{5}{4}x+\frac{1}{4}=0$

$\Rightarrow 4x^2-5x+1=0$

Hence, D is the correct option.