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# If the Equations X 2 + 2 X + 3 λ = 0 and 2 X 2 + 3 X + 5 λ = 0 Have a Non-zero Common Roots, Then λ = - Mathematics

MCQ

If the equations $x^2 + 2x + 3\lambda = 0 \text { and } 2 x^2 + 3x + 5\lambda = 0$  have a non-zero common roots, then λ =

#### Options

• 1

• -1

• 3

• none of these.

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#### Solution

-1

Let $\alpha$ be the common roots of the equations, $x^2 + 2x + 3\lambda = 0$ and $2 x^2 + 3x + 5\lambda = 0$

Therefore,

$\alpha^2 + 2\alpha + 3\lambda = 0$      ... (1)

$2 \alpha^2 + 3\alpha + 5\lambda = 0$       ... (2)

Solving (1) and (2) by cross multiplication, we get

$\frac{\alpha^2}{10\lambda - 9\lambda} = \frac{\alpha}{6\lambda - 5\lambda} = \frac{1}{3 - 4}$

$\Rightarrow \alpha^2 = - \lambda, \alpha = - \lambda$

$\Rightarrow - \lambda = \lambda^2$

$\Rightarrow \lambda = - 1$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 14 Quadratic Equations
Q 15 | Page 17
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