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Question

If the equations x2+2x+3λ=0 and 2x2+3x+5λ=0 have a non-zero common roots, then λ =
(a) 1
(b) −1
(c) 3
(d) none of these.

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Solution

(b) −1

Let α be the common roots of the equations, x2 + 2x + 3λ = 0 and 2x2 + 3x + 5λ =0

Therefore,

α2 + 2α + 3λ = 0 ... (1)

2α2 + 3α + 5λ = 0 ... (2)

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

α210λ-9λ=α6λ-5λ=13-4α2=-λ, α=-λ-λ=λ2λ=-1

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