If the equation 2x2 - 3x -5- - 0 and x2 - 2x - 3- - 0 have a common root- then -

Given equations 2x^2 + 3x + 5λ = 0 and x^2 + 2x + 3λ = 0 nbsp; have a common root. Solving by cross multiplication method x^2 λ= x λ = 11 ⇒ x^2 = λ, x= ...

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Standard XI

Mathematics

Quadratic Equations with Exactly One Root Common

If the equati...

Question

If the equation $2 x^{2} + 3 x + 5 λ = 0$ and $x^{2} + 2 x + 3 λ = 0$ have a common root, then $λ =$

- 1

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Solution

The correct option is D $0, - 1$
Given equations $2 x^{2} + 3 x + 5 λ = 0$ and $x^{2} + 2 x + 3 λ = 0$ have a common root.

Solving by cross multiplication method

$\frac{x^{2}}{- λ} = \frac{x}{- λ} = \frac{1}{1}$
$\Rightarrow x^{2} = - λ, x = - λ$
$\Rightarrow λ^{2} = - λ \Rightarrow λ = - 1, 0$

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If the equation 2x2 + 3x +5λ=0 and x2+2x+3λ=0 have a common root, then λ=

The correct option is D 0,−1Given equations 2x2+3x+5λ=0 and x2+2x+3λ=0 have a common root. Solving by cross multiplication method x2−λ=x−λ=11 ⇒x2=−λ,x=−λ ⇒λ2=−λ⇒λ =−1,0

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