Question

Let a, b, c be real numbers such that $a + b + c < 0$ and the quadratic equation $ax^2 + bx + c = 0$ has imaginary roots. Then

• A. $a > 0, c > 0$
• B. $a > 0, c < 0$
• C. $a < 0, c > 0$
• D. $a < 0, c < 0$

Answer 1

Answer: (D)

$a < 0, c < 0$

Answer 2

$f\left(x\right) = ax^{2}+bx+c, \,f\left(1\right) < 0\,so\,f\left(x\right) < 0 \,\forall\, x \in R \Rightarrow f\left(0\right) < 0 \Rightarrow c < 0 \Rightarrow a < 0\,and\,c < 0$