Let $f(x)$ be a non-constant polynomial with real coefficients such that $f\left(\frac{1}{2}\right)=100$ and $f(x) \leq 100$ for all real $x$. Which of the following statements is NOT necessarily true?
Let $f(x)$ be a non-constant polynomial with real coefficients such that $f\left(\frac{1}{2}\right)=100$ and $f(x) \leq 100$ for all real $x$. Which of the following statements is NOT necessarily true?
- [KVPY 2013]
- A
The coefficient of the highest degree term in $f(x)$ is negative.
- B
$f(x)$ has at least two real roots.
- C
If $x \neq 1 / 2$ then $f(x) < 100$.
- D
At least one of the coefficients of $f(x)$ is bigger than $50.$
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