JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
The number of distinct real roots of the equation \(x ^{7}-7 x -2=0\) is
- A \(5\)
- B \(7\)
- C \(1\)
- D \(3\)
Answer & Solution
Correct Answer
(D) \(3\)
Step-by-step Solution
Detailed explanation
\(x^{7}-7 x-2=0\) \(x^{7}-7 x=2\) \(f(x)=x^{7}-7 x \text { (odd) } and \,y=2\) \(f(x)=x\left(x^{2}-7^{1 / 3}\right)\left(x^{4}+x^{2} \cdot 7^{1 / 3}+7^{2 / 3}\right)\) \(f^{\prime}(x)=7\left(x^{6}-1\right)=7\left(x^{2}-1\right)\left(x^{4}+x^{2}+1\right)\)…
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