Question

If the quadratic $a{x}^2+bx+c=0$, where $a>0$, has both imaginary roots, then

• A. $a+b+c>0$
• B. $a-b+c<0$
• C. $a+b+c<0$
• D. None of these

Answer 1

The correct option is B $a-b+c<0$

$y=f\left(x\right)=a{x}^2+bx+c=0$

Since $f\left(x\right)$ has imaginary roots

$y>0$

$f\left(x_i\right)>0$

$f\left(1\right)>0,\Rightarrow a+b+c>0$

must also be true

$f(-1)>0,\Rightarrow a-b+c>0$