Question:
<p>If f(x) = ax<sup>2</sup> +bx + c has no real zeros and a + b + c < 0, then</p>
<p style="display:inline">c > 0</p>
<p style="display:inline">c = 0</p>
<p style="display:inline">c < 0</p>
<p style="display:inline">C ≥ 0</p>
Step-by-Step Solution
Key Concept: A quadratic function with no real zeros maintains a constant sign for all real x, meaning the sign of any single value like f(1) determines the sign of the entire function.
<p>We are given a+b+c < 0<br />
<span class="math-tex">$\Rightarrow \quad f(1)<0$</span><br />
So, f(x) must be negative for all x.<br />
<br />
</p>
Correct Answer: C