Question

The quadratic expression $a{x}^2+bx+c>0\forall xϵR$, then which of the following option(s) is/are correct ?

• A. $13a–5b+2c>0$
• B. $13a–b+2c>0$
• C. $c>0,D<0$
• D. $a+c>b,D<0$

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A $13a–5b+2c>0$
B $13a–b+2c>0$
C $c>0,D<0$
D $a+c>b,D<0$

$a{x}^2+bx+c>0\forall xϵR\Rightarrow a>0,D<0f\left(0\right)=c>0f(-1)=a-b+c>0\Rightarrow a+c>bf(-3)+f(-2)=13a-5b+2c>0f(-3)+f\left(2\right)=13a-b+2c>0$