Question

The difference between the corresponding roots of the equations $x^2+ax+b=0$ and $x^2+bx+a=0$ is same, then

• A. $a+b-4=0$
• B. $a-b+4=0$
• C. $a+b+4=0$
• D. None of these

Answer 1

The correct option is C $a+b+4=0$

Let $x_1$ & $x_2$ be the roots of the equation $x^2+ax+b=0$
Therefore, $x_1+x_2=-a$ and $x_1{x}_2=b$
and $y_1$ & $y_2$ be the roots of the equation $x^2+bx+a=0$
Therefore, $y_1+y_2=-b$ and $y_1{y}_2=a$
Given that, $x_1-x_2=y_1-y_2$
$\Rightarrow {(x_1+x_2)}^2-4x_1{x}_2={(y_1+y_2)}^2-4y_1{y}_2$
$\Rightarrow a^2-4b=b^2-4a$
$\Rightarrow (a-b)(a+b+4)=0$
Therefore, $a-b=0$ or $a+b+4=0$
Ans: C