JEE Mains · Maths · STD 12 - 6. Application of derivatives
The number of real solutions of \(x^{7}+5 x^{3}+3 x+1=\) \(0\) is equal to............
- A \(0\)
- B \(1\)
- C \(3\)
- D \(5\)
Answer & Solution
Correct Answer
(B) \(1\)
Step-by-step Solution
Detailed explanation
\(f(x)=x^{7}+5 x^{3}+3 x+1\) \(f^{\prime}(x)=7 x^{6}+15 x^{2}+3>0\) \(\therefore f ( x )\) is strictly increasing function \(x \rightarrow-\infty, y \rightarrow-\infty\) \(x \rightarrow \infty, y \rightarrow \infty\) \(\therefore\) no. of real solution \(=1\)
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