• # question_answer If the equations $2{{x}^{2}}+3x+5\lambda =0$ and ${{x}^{2}}+2x+3\lambda =0$ have a common root, then $\lambda =$ [RPET 1989] A) 0 B) -1 C) $0,-1$ D) 2,-1

Solution :

Given equations are $2{{x}^{2}}+3x+5\lambda =0$ and ${{x}^{2}}+2x+3\lambda =0$ have a common root if $\frac{{{x}^{2}}}{-\lambda }=\frac{x}{-\lambda }=\frac{1}{1}$ Þ ${{x}^{2}}=-\lambda ,x=-\lambda$or $\lambda =-1,\,\,0$.

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