Question

If the roots of the equation $x^2+px+c=0$ are $2,-2$ and the $x^2+bx+q=0$ are $-1,-2$, then the roots of the equation $x^2+bx+c=0$ are

• A. -3 ,-2
• B. -3 ,2
• C. 1 ,- 4
• D. -5, 1
• E. - 1 ,4

Answer 1

Answer: (C)

Given, roots of the equation $x^2+px+c=0$ are 2 and $-2$.
$\therefore -p=2-2$
$\Rightarrow p=0$
and $(2)\cdot (-2)=c$
$\Rightarrow c=-4$
Again, roots of the equation $x^2+bx+q=0$ are $-1$ and $-2$
$\therefore -b=-1-2$
$\Rightarrow b=3$
and $(-1)\cdot (-2)=q$
$\Rightarrow q=2$
$\therefore x^2+bx+c\equiv x^3+3x-4=0$
$\Rightarrow (x-1)(x+4)=0$
So, the required roots are $1$ and $-4$