Question

Find $k$, if the equations $4x^2-11x+2k=0$ and $x^2-3x-k=0$ have a common root.

• A. $0$
• B. $\frac{-17}{36}$
• C. $-\frac{17}{6}$
• D. $\pm \frac{17}{6}$

Answer 1

Answer: (A), (B)

The correct options are
A $0$
B $\frac{-17}{36}$

Let $\alpha$ is the common root the equation $4x^2-11x+2k=0$ ...(1)

and $x^2-3x-k=0$ ...(2)

then $\alpha$ will satisfy both of these equations.

Equation (1) $\Rightarrow {4\alpha }^2-11\alpha +2k=0$ ...(3)
Equation (2) $\Rightarrow {\alpha }^2-3\alpha -k=0\Rightarrow {2\alpha }^2-6\alpha -2k=0$ ....(4)
Adding (3) and (4), we get
${6\alpha }^2-17\alpha =0\Rightarrow \alpha =0,\frac{17}{6}\Rightarrow k=0,\frac{-17}{36}$

Hence option (A) and (B) are coorect.