jee-advanced 2014 Q44

jee-advanced · India · paper1 Stationary points and optimisation Count or characterize roots using extremum values

Let $a \in \mathbb{R}$ and let $f : \mathbb{R} \rightarrow \mathbb{R}$ be given by $$f(x) = x^5 - 5x + a$$ Then
(A) $f(x)$ has three real roots if $a > 4$
(B) $f(x)$ has only one real root if $a > 4$
(C) $f(x)$ has three real roots if $a < -4$
(D) $f(x)$ has three real roots if $-4 < a < 4$

Let $a \in \mathbb{R}$ and let $f : \mathbb{R} \rightarrow \mathbb{R}$ be given by
$$f(x) = x^5 - 5x + a$$
Then\\
(A) $f(x)$ has three real roots if $a > 4$\\
(B) $f(x)$ has only one real root if $a > 4$\\
(C) $f(x)$ has three real roots if $a < -4$\\
(D) $f(x)$ has three real roots if $-4 < a < 4$

Paper Questions

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