Question

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

• A. is positive
• B. is negative
• C. is zero
• D. depends on the value of $b$

Answer 1

The correct option is A is positive

The quadratic equation $a{x}^2-bx+1=0$ has imaginary roots.
Hence, the expression $a{x}^2-bx+1$ is either positive for all values of $x$ or negative for all values of $x$.
When $x=0$, $a{x}^2-bx+1=1>0$
Hence, $a{x}^2-bx+1>0$ for all values of $x$
When $x=-1$ ,
$a{x}^2-bx+1=a+b+1>0$
Hence, option A is correct.