Question

Find $m$, so that the equation $3x^2-2mx-4=0$ and $x^2-4mx+2=0$ may have a common root. Can the equations have a common non-real root?

• A. $3$
• B. $-3$
• C. $4$
• D. No solution

Answer 1

The correct option is D No solution

Given that,

$\begin{array}{c}3x^2-2mx-4=0--------\left(i\right)\\ x^2-4mx+2=0---------\left(ii\right)\end{array}$

From $\left(i\right)$ and $\left(ii\right)$ equations

$\begin{array}{c}{\left(-2m\right)}^2+4\times 3\times 4={\left(-4m\right)}^2-4\times 1\times 2\\ 14m^2+24=16m^2-8\\ 14m^2-16m^2=18-24\\ -4m^2=-32\\ m^2=\frac{32}{4}\\ m^2=8\\ m=\sqrt{8}\\ \end{array}$

Hence,

None of these