JEE Main202227 Jun 2022Morning ShiftMathematicsApplication of DerivativesActual

The number of distinct real roots of x 4 - 4 x + 1 = 0 is

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Correct answer

C. 2

Step-by-step solution

Let f x = x 4 - 4 x + 1 f ' x = 4 x 3 - 4 and f ' x = 0 ⇒ x = 1 So the extrema of the function is at x = 1 Plotting the graph we get f '' x = 12 x 2    ∴   f '' 1 > 0 And at x = 1 ,   f 1 = - 2 < 0 So, graph of f x will cut x-axis at two points, ∴ Number of real roots of f x = 0 is equal to 2

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