The number of real roots of the equation \( x^{5}+3 x^{3}+4 x+30=0 \) is

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Question: Answered & Verified by Expert

The number of real roots of the equation \( x^{5}+3 x^{3}+4 x+30=0 \) is

MathematicsQuadratic EquationJEE Main

Options:

A \( 1 \)
B \( 2 \)
C \( 3 \)
D \( 5 \)

Solution:

1764 Upvotes Verified Answer

The correct answer is: \( 1 \)

Let

f (x) = x^{5} + 3 x^{3} + 4 x + 30

\Rightarrow f^{'} (x) = 5 x^{4} + 9 x^{2} + 4

\Rightarrow f^{'} (x) > 0

for all

x \in R

Hence, the

f (x) = 0

has only one real root.

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