Question

If a, b, c $\in$ R and a $\ne$ 0, c < 0, and if the quadratic equation $a{x}^2+bx+c$ = 0 has imaginary roots, then a + b + c is

• A. Negative
• B. Zero
• C. Can't say

Answer 1

The correct option is A

Negative

Let y = $a{x}^2+bx+c$
It's given that $a{x}^2+bx+c$ = 0 has only imaginary roots. That means the graph of y = $a{x}^2+bx+c$ does not touch the x-axis.
It either completely lies above the x-axis or lies below the x-axis. We are given c<0. c is the value of y when x = 0.
That means the graph lies completely below x-axis or the value of y = $a{x}^2+bx+c$ is less than zero for any value of x.
It is less than zero for x = 1 also. Value of y when x = 0 is a+b+c
That means a+b+c < 0.