Question

If $x^2$ + 2ax + 10 - 3a > 0 for each $xϵR$, then

• A. a < -5
• B. -5 < a < 2
• C. a > 5
• D. 2 < a <5

Answer 1

The correct option is B

-5 < a < 2

$x^2+2ax+10-3a$> $0\forall xϵR$

$\Rightarrow (x+a{)}^2-(a^2+10-3a)$ > $0\forall xϵR$

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

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

$\Rightarrow$ -5 < a<2