Question

If the graph of the function $y=16x^2+8(a+5)x-7a-5$ is strictly above the $x$-axis, then $a$ must satisfy the inequality

• A. $-15<a<-2$
• B. $-2<a<-1$
• C. $5<a<7$
• D. none of these

Answer 1

The correct option is A $-15<a<-2$

Given that curve lies above $x$ axis, it means $\Delta <0$
$\Rightarrow$$64(a+5{)}^2+64(7a+5)<0$
$(a+2)(a+15)<0$
$-15<a<2$.