Let a, b, c be real numbers such that a + b + c

Question

Let a, b, c be real numbers such that a + b + c < 0 and the quadratic equation ax2 + 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

Tardigrade Admin · Accepted Answer

f(x) = ax2+bx+c, f(1) < 0 so f(x) < 0 ∀ x ∈ R ⇒ f(0) < 0 ⇒ c < 0 ⇒ a < 0 and c < 0

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

$a > 0, c > 0$

$a > 0, c < 0$

$a < 0, c > 0$

$a < 0, c < 0$

$f (x) = a x^{2} + b x + c, f (1) < 0 so f (x) < 0 \forall x \in R \Rightarrow f (0) < 0 \Rightarrow c < 0 \Rightarrow a < 0 an d c < 0$

Q. Let a, b, c be real numbers such that a+b+c<0 and the quadratic equation ax2+bx+c=0 has imaginary roots. Then

a>0,c>0

a>0,c<0

a<0,c>0

a<0,c<0