Question

(a) Find k if the equations $4x^2-11x+2k=0$ and $x^2-3x-k=0$ have a common root and obtain the common root for this value of k.

Answer 1

(a) $\frac{{\alpha }^2}{17k}=\frac{\alpha }{6k}=\frac{1}{-1}$
$\therefore$ ${\left(6k\right)}^2=17k(-1)$ or $k(36k+17)=0$
$\therefore$ $k=0$ and $-17/36$.
Also from (1),
$\alpha =\frac{17k}{6k}=\frac{17}{6}$ or $\alpha =\frac{6k}{-1}=0$ or $\frac{17}{6}$.
Hence the common root is either zero or $17/6$.