Question

If the equations $x^2 + ax + bc = 0$ and $x^2 + bx + ca = 0$ have a common root and if $a$, $b$ and $c$ are non zero distinct real numbers, then their other roots satisfy the equation

• A. $x^2 + x + abc = 0$
• B. $x^2 -(a+b)x+ab= 0$
• C. $x^2 +(a+b)x+ab= 0$
• D. $x^2+x+ab=0$
• E. $x^2 +abx + abc = 0$

Answer 1

Answer: (B)

Given equations are
$x^{2}+a x+b c=0 $
and $x^{2}+b x+c a=0$
On subtracting equation second from equation first
$\therefore (a-b) x+c(b-a)=0$
$\Rightarrow (a-b)(x-c)=0$
$\Rightarrow x=c$ is the common root.
Thus, the roots of $x^{2}+a x+b c=0$ are $b$ and $c$ and that of
$x^{2}+b x+c a=0$ are $c$ and $a$.
It roots band $Q$, then equation will be
$x^{2}-(a+b) x+a b=0$