If a, b, c ∈ R and quadratic equation x2+(a+b) x+c=0 has no real roots then

Question

If a, b, c ∈ R and quadratic equation x2+(a+b) x+c=0 has no real roots then (A) c(a+b+c) > 0 (B) c+c(a+b+c) > 0 (C) c+c(a+b-c) > 0 (D) c(a+b-c) > 0

Tardigrade Admin · Accepted Answer

Since f(x) has no real roots, f(x) has same sign for every x ∴ f(0) ⋅ f(1)>0

Q. If $a, b, c \in R$ and quadratic equation $x^{2} + (a + b) x + c = 0$ has no real roots then