Question

If $a,b\in R,a>0$ and the quadratic equation $a{x}^2-bx+1=0$ has imaginary roots, then
$a+b+1$ is

• A. positive
• B. negative
• C. zero
• D. depends on the sign of b.

Answer 1

The correct option is A positive

$f\left(x\right)=a{x}^2-bx+1$
$f\left(0\right)=1$ (positive)
$i.e.f\left(x\right)=a{x}^2-bx+1>0(givena{x}^2-bx+1=0hasimaginaryroots)$
$f(-1)=a+b+1>0$