Let a \in R and let f : R → R be given by f(x) = x5

Engineering

Mathematics

Roots of a Cubic

Question

Let a $\in$ R and let f : R → R be given by f(x) = x⁵ – 5x + a.

Then

f(x) has three real roots if a > 4.

f(x) has three real roots if a < – 4.

f(x) has three real roots if – 4 < a < 4.

f(x) has only one real root if a > 4.

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a = 5x – x⁵ = f(x)

Now, graph of f(x) = 5x – x⁵.

From the graph ⇒ (B) & (D)