Question

Find a quadratic equation whose product of roots $x_1$ and $x_2$ is equal to $4$ and satisfying the relation $\frac{x_1}{x_1-1}+\frac{x_2}{x_2-1}=2$.

• A. $x^2-2x+4=0$
• B. $x^2-3x+4=0$
• C. $x^2-2x+3=0$
• D. $x^2-3x+2=0$

Answer 1

Answer: (A)

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

Simplifying the expression, we get
$x_1.x_2-x_1+x_2{x}_1-x_2=2(x_1{x}_2-(x_1{x}_2)+1)$
$2(x_1.x_2)-(x_1+x_2)=2x_1{x}_2-2(x_1+x_2)+2$
$x_1+x_2=2$
And $x_1.x_2=4$
Hence, the required equation with roots $x_1$ and $x_2$ is
$x^2-2x+4=0$.