Question

If the equations $x^2+2x+3\lambda =0and2x^2+3x+5\lambda =0$have a non-zero common roots, then $\lambda =$

• A. 1
• B. -1
• C. 3
• D. none of these

Answer 1

Let a be the common roots of the equations $x^2+2x+3\lambda =0and2x^2+3x+5\lambda =0$ Therefore, $\frac{{\alpha }^2}{10\lambda -9\lambda }=\frac{\alpha }{6\lambda -5\lambda }=\frac{1}{3-4}$ $\Rightarrow {\alpha }^2=-\lambda ,\alpha =-\lambda$ $\Rightarrow \lambda =-1$