Question

Find the value of $k$ so that the equations $x^2-x-12=0$ and $k{x}^2+10x+3=0$ may have one root in common. Also find the common root.

Answer 1

Given: $x^2-x-12=0$

$\Rightarrow x^2-4x+3x-12=0$

$\Rightarrow x(x-4)+3(x-4)=0$

on solving we get $x=-3$ and $x=4$

since one root of this equaiton is root of $k{x}^2+10x+3=0$

so putting $x=-3$ in this equation , we get

$\Rightarrow 9k-30+3=0$

$\therefore k=3$

putting $x=4$ , we get

$16k+40+3=0$

$\Rightarrow k=\frac{-43}{16}$