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CGP EDU Academic Team
Published on: August 13, 2026
Let a ∈ R and let f : R → R be given by f(x) = x 5 – 5x + a. Then
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CHECK THE SOLUTION.
(b,d)
Sol. f(x) = x 5 – 5x + a = 0
x 5 – 5x = –a
x(x 4 – 5) = –a
x(x 2 – 
)(x 2 + 
) = –a
x(x – 5 1/4 )(x + 5 1/4 )(x 2 + 
) = –a ..(1)
f'(x) = 5x 4 – 5 = 0
(x 2 –1)(x 2 + 1) = 0
(x – 1)(x +1)(x 2 + 1) = 0
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