Question

If ax² + bx + c, a, b, c Ī R has no real zeros, and if c < 0, then

• A. a < 0
• B. a + b + c > 0
• C. a > 0
• D. None of these

Answer 1

Answer: (A)

a < 0

Answer 2

Let f(x) = ax² + bx + c. Since f(x) has no real zeros, either f(x) > 0 or f(x) < 0 for all x Ī R. Since f(0) = c < 0, we get f(x) < 0 " x Ī R. Therefore, a < 0 as the parabola y = f (x) open downwards.