Question

If the range of $a$ for which is
$a{x}^2+3x+4>0,\forall x\in R$ is $(\frac{m}{16},\infty )$.Find $m$

Answer 1

Equation is greater than zero

$\Rightarrow$descriminant of the quadratic equation must be less than zero .i.e. equation has no real roots

$\Rightarrow 3^2<4\times a\times 4$

$\Rightarrow a>\frac{9}{16}$

$\Rightarrow a\in (\frac{9}{16},\infty )$