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Question

if the equations \( 2x^2 + 3x + 5λ = 0\) and \( x^2 + 2x + 3λ = 0 \) have a common root, then λ =

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Solution

\(Solving~2x^2+3x+5 \lambda=0~and~x^2+2x+3 \lambda =0\\
x=- \lambda\\
Substituting~in~first~equation~2 \lambda^2+3 (-\lambda)+ \lambda 5=0\\
\therefore~\lambda=0,-1\)


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