Q5 / 82 · NTA Abhyas (JEE Main) 2020 · Mathematics · Quadratic Equation

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

A
$7 x^{2} - 1 = 0$
Correct answer
B
$7 x^{2} + 1 = 0$
C
$7 x^{2} + 2 = 0$
D
$7 x^{2} - 2 = 0$

Solution

Replace

x

by

2 (\frac{1 + x}{1 - x})

4 {(\frac{1 + x}{1 - x})}^{2} - 3 (2 (\frac{1 + x}{1 - x})) + 4 = 0

\Rightarrow 7 x^{2} + 1 = 0

Hence, the correct answer is option: 'B'.

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