First slide

Theory of equations

Question

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

Moderate

A

$- 5 < a < 2$
B

$a < - 5$
C

$a > 5$
D

$2 < a < 5$

Solution

According to given condition,
$4 a^{2} - 4 (10 - 3 a) < 0 \Rightarrow a^{2} + 3 a - 10 < 0$
$\Rightarrow (a + 5) (a - 2) < 0 \Rightarrow - 5 < a < 2 .$

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