Question

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

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

Answer 1

The correct option is A

$-5<a<2$

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

$\Rightarrow (x+a{)}^2-(a^2-10+3a)>0\forall x\in R$
For $\Delta >0$,

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

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

$\Rightarrow -5<a<2$