Question

If the equations $x^2-x-12=0andk{x}^2+10x+3=0$ may have one common root, then k =

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

Let $\alpha$ be a common roots, then

${\alpha }^2-\alpha -12-0,k{\alpha }^2+10\alpha +3=0$ .

$\frac{{\alpha }^2}{117}=\frac{\alpha }{-12k-3}=\frac{1}{10+k}$

$\therefore$ $\Rightarrow$ $(12k+3{)}^2=117(10+k)$

$\Rightarrow (k-3)(16k+43)=0$ $\Rightarrow k=3or\frac{-43}{16}$ .