Question

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

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

Answer 1

The correct option is B -5 < a < 2

$x^2+2ax+10-3a>0\forall x$

$\Rightarrow D<0$
$\Rightarrow 4a^2-4(10-3a)<0$
$\Rightarrow a^2+3a-10<0$
$\Rightarrow (a+5)(a-2)<0$
$\Rightarrow aϵ(-5,2)$