If α , β are the roots of the equation x2 -3x+4=0 , then the equation whose roots are (α - 2/α + 2), (β - 2/β + 2) is

Question

If α , β are the roots of the equation x2 -3x+4=0 , then the equation whose roots are (α - 2/α + 2), (β - 2/β + 2) is (A) 7x2 -1=0 (B) 7x2+1=0 (C) 7x2+2=0 (D) 7x2 -2=0

Tardigrade Admin · Accepted Answer

Replace x by 2((1+x/1-x)) 4((1+x/1-x))2-3(2((1+x/1-x)))+4=0 ⇒ 7 x2+1=0

Q. 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

$7 x^{2} - 1 = 0$

$7 x^{2} + 1 = 0$

$7 x^{2} + 2 = 0$

$7 x^{2} - 2 = 0$

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

Q. If α,β are the roots of the equation x2−3x+4=0 , then the equation whose roots are α+2α−2​,β+2β−2​ is

7x2−1=0

7x2+1=0

7x2+2=0

7x2−2=0