If one root of the quadratic equation $a x^{2} + b x + c = 0$ is double the other then which one of the following is correct

b^{2} = 3 a c

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2 b^{2} = 5 a c

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2 b^{2} = 9 a c

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2 b^{2} > 9 a c

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Solution

The correct option is C $2 b^{2} = 9 a c$
Let $m$ be the one root of given equation then the other root be $2 m$ .
Then $3 m = - \frac{b}{a} o r m = - \frac{b}{3 a}$
Now $m (2 m) = \frac{c}{a}$
$(\frac{- b}{3 a}) (\frac{- 2 b}{3 a}) = \frac{c}{a}$
$∴ 2 b^{2} = 9 a c$

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