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Complex Numbers

If a x2+b x+c...

Question

If $a x^{2} + b x + c = 0 a n d b x^{2} + c x + a = 0$ have a common root and a,b,c are non - zero real numbers then $\frac{a^{3} + b^{3} + c^{3}}{a b c}$ is equal to :

A

1

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B

2

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C

3

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D

None

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Solution

The correct option is C
3

$a x^{2} + b x + c = 0 a n d b x^{2} + c x + a = 0$ has a common root, then

$\frac{x^{2}}{a b - c^{2}} = \frac{x}{c b - a^{2}} = \frac{1}{a c - b^{2}}$

$\Rightarrow$ $(c b - a^{2})^{2} = (a b - c^{2}) (a c - b^{2})$

$\Rightarrow$ $a^{3} + b^{3} + c^{3} = 3 a b c$

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Similar questions

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