If the equations x 2 + 2 x + 3 = 0 and a x 2 + b x + c = 0 , a , b , c ∈ R , have a common root, then a : b : c is:

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MathematicsQuadratic EquationCommon RootsMedium2 minPYQ_2013

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If the equations $x^{2} + 2 x + 3 = 0$ and $a x^{2} + b x + c = 0,$ $a, b, c \in R,$ have a common root, then $a : b : c$ is:

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Answer:

Solution:

As the roots of $x^{2} + 2 x + 3 = 0$ are imaginary, hence both the roots are common with $a x^{2} + b x + c = 0$ .

$∴ \frac{a}{1} = \frac{b}{2} = \frac{c}{3}$ .

Stream:JEESubject:MathematicsTopic:Quadratic EquationSubtopic:Common Roots

⏱ 2mℹ️ Source: PYQ_2013

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