﻿ If ax2 + bx + c, a, b, c Ïµ R has no real zeros, and if c < 0, then, : Kaysons Education

# If ax2 + bx + c, a, b, c Ïµ R has No Real Zeros, And If c < 0, Then,

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## Question

### Solution

Correct option is

a < 0

Let f (x) = ax2 + bx + c. Since f (x) has no real zeros, either f (x) > 0 orf (x) < 0 for all x Ïµ R. Since f (0) = c < 0, we get f (x) < 0 ∀ x Ïµ R. therefore a < 0 as the parabola y = f (x) must open downwards.

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