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Sign of Quadratic Expression

If x2+ax+10...

Question

If $x^{2} + a x + 10 = 0$ and $x^{2} + b x - 10 = 0$ have a common root, then $a^{2} - b^{2}$ is equal to

A

10

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B

20

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C

30

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D

40

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Solution

The correct option is A $10$
Applying common root condition

$\Rightarrow (10.1 - (- 10.1))^{2} = (- 10 a - 10 b) (b - a)$

$\Rightarrow 100 = 10 (a + b) (a - b)$

$\Rightarrow a^{2} - b^{2} = 10$

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