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Properties of Inverse Function

If x 2 +2ax...

Question

If $x^{2} + 2 a x + 10 - 3 a > 0$ for all $x \in R$ , then

- 5 < a < 2

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a < - 5

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a > 5

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2 < a < 5

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Solution

The correct option is A $- 5 < a < 2$
Given equation is $x^{2} + 2 a x + 10 - 3 a > 0$

According to the given condition, we have

$4 a^{2} - 4 (10 - 3 a) < 0$

$\Rightarrow a^{2} + 3 a - 10 < 0$

$\Rightarrow (a + 5) (a - 2) < 0$

$\Rightarrow - 5 < a < 2$

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