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Strictly Increasing Functions

For all x, ...

Question

For all $x, x^{2} + 2 a x + 10 - 3 a > 0$ , then the interval in which $a$ lies is

A

a < 5

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B

- 5 < a < 2

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C

a > 5

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D

2 < a < 5

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Solution

The correct option is B $- 5 < a < 2$
$x^{2} + 2 a x + 10 - 3 a > 0 f o r a l l x ∴ d i s c r i m i n a n t i s l e s s t h a n 0 4 a^{2} - 4 (10 - 3 a) < 0 a^{2} + 3 a - 10 < 0 (a + 5) (a - 2) < 0 a \in (- 5, 2)$

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