JEE Main202224 Jun 2022Evening ShiftMathematicsApplication of DerivativesActual

The number of distinct real roots of the equation x 7 - 7 x - 2 = 0 is

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Correct answer

D. 3

Step-by-step solution

Given, x 7 - 7 x - 2 = 0 x 7 - 7 x = 2 Now taking f x = x 7 - 7 x (odd) & y = 2 Now differentiating f x w.r.t x we get, f ' x = 7 x 6 - 1 = 7 x 2 - 1 x 4 + x 2 + 1 f ' x = 0 ⇒ x = ± 1 So points of extrema are - 1   &   1   , Now plotting the graph to check number of solution we get, f x = 2 has 3 real distinct solution.

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