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JEE Main202226 Jul 2022Morning ShiftMathematicsApplication of DerivativesActual

The number of distinct real roots of the equation x 5 x 3 - x 2 - x + 1 + x 3 x 3 - 4 x 2 - 2 x + 4 - 1 = 0 is

Correct answer

3

Step-by-step solution

Given, x 5 x 3 - x 2 - x + 1 + x 3 x 3 - 4 x 2 - 2 x + 4 - 1 = 0 Now on rearranging we get ⇒ x 8 - x 7 - x 6 + x 5 + 3 x 4 - 4 x 3 - 2 x 2 + 4 x - 1 = 0 ⇒ x 7 x - 1 - x 5 x - 1 + 3 x 3 x - 1 - x x 2 - 1 - 2 x x - 1 + x - 1 = 0 ⇒ x - 1 x 7 - x 5 + 3 x 3 - x x + 1 - 2 x + 1 = 0 ⇒ x - 1 x 5 x 2 - 1 + 3 x x 2 - 1 - 1 x 2 - 1 = 0 ⇒ x 2 - 1 x - 1 x 5 + 3 x - 1 = 0 From above equation it is clearly visible that the root are x = ± 1 and for x 5 + 3 x - 1 Let f x = x 5 + 3 x - 1 , f ' x =

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