Aspire Faculty ID #15157 · Topic: JAMIA MCA 2017 · Just now
JAMIA MCA 2017

If the equations $x^2 + 2x + 3\lambda = 0$ and $2x^2 + 3x + 5\lambda = 0$ have a non-zero common root, then $\lambda$ is equal to

Solution

Let the common root be $x$. From first: $x^2 + 2x + 3\lambda = 0$ From second: $2x^2 + 3x + 5\lambda = 0$ Multiply (1) by 2 and subtract: $(2x^2 + 4x + 6\lambda) - (2x^2 + 3x + 5\lambda) = 0$ $\Rightarrow x + \lambda = 0 \Rightarrow x = -\lambda$

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