Question

If the equations $4x^2-x-1=0$ and $3x^2+(\lambda +\mu )x+\lambda -\mu =0$ have a root common then the rational values of $\lambda$ and $\mu$ are

• A. $\lambda =\frac{-3}{4}$
• B. $\lambda =0$
• C. $\mu =\frac{3}{4}$
• D. $\mu =0$

Answer 1

Answer: (A), (D)

The correct options are
A $\lambda =\frac{-3}{4}$
D $\mu =0$

Roots of $4x^2-x-1=0$ are irrational.

$x=\frac{1\pm \sqrt{17}}{8}$

So, one root common implies both roots are common.

Therefore,

$\frac{4}{3}=\frac{-1}{\lambda +\mu }=\frac{-1}{\lambda -\mu }$

$\Rightarrow \lambda =\frac{-3}{4},\mu =0$