Question

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

• A. $10x^2-11x+2=0$
• B. $10x^2+11x+2=0$
• C. $11x^2-10x+2=0$
• D. $x^2+11x+10=0$

Answer 1

The correct option is B $10x^2+11x+2=0$

As $\alpha ,\beta$ are roots of $2x^2+3x-4=0$ ...........................$\left(i\right)$
We need the equation whose roots are $\frac{1}{\alpha -2}$ and $\frac{1}{\beta -2}$.
Setting $y=\frac{1}{\alpha -2}\Rightarrow \alpha =2+\frac{1}{y}$
Putting the value of $\alpha$ in $\left(i\right)$, we get
$2{(2+\frac{1}{y})}^2+3(2+\frac{1}{y})-4=0$
$\therefore 10y^2+11y+2=0or10x^2+11x+2=0$
Hence, choice (B) is correct answer.