Question

If $x^2-11x+k=0$ and $x^2-14x+2k=0$ have a common root,then $k$ =

• A. $1$
• B. $12$
• C. $24$
• D. $32$

Answer 1

The correct option is C $24$

Let, $\alpha ,\beta$ be the roots of the following equation.

$x^2-11x+k=0$

$\alpha +\beta =-\frac{B}{A}=-\frac{-11}{1}=11$.....(1)

$\alpha \beta =\frac{C}{A}=\frac{K}{1}=K$.....(2)

Let, $\alpha ,\gamma$ be the roots of the following equation.

$x^2-14x+2k=0$

$\alpha +\gamma =-\frac{B}{A}=-\frac{-14}{1}=11$.....(3)

$\alpha \gamma =\frac{C}{A}=\frac{2K}{1}=2K$.....(4)

using (1), (2), (3) and (4), we get,

$\alpha =8,\beta =3,\gamma =6$

$K=\alpha \beta =8\times 3=24$