Question

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

• A. $7x^{2} \, -1=0$
• B. $7x^{2}+1=0$
• C. $7x^{2}+2=0$
• D. $7x^{2} \, -2=0$

Answer 1

Answer: (B)

Replace $x$ by $2\left(\frac{1+x}{1-x}\right)$
$4\left(\frac{1+x}{1-x}\right)^{2}-3\left(2\left(\frac{1+x}{1-x}\right)\right)+4=0$
$\Rightarrow 7 x^{2}+1=0$