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Nature of Roots of a Cubic Polynomial Using Derivatives

16. The maxim...

Question

16. The maximum number of real roots of the equation x2n -1 = 0 is
(1) 2 (2) 3 (3) n (4) 2n

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Solution

The maximum number of real roots of the equation x²ⁿ -1 = 0 is 2n.

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Q. The maximum number of real roots of the equation

x^{2 n} - 1 = 0

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(x - 1)^{2} + (x - 2)^{2} + (x - 3)^{2} + (x - 4)^{2} + . . . . . + (x - n)^{2} = 0

Q. Assertion :The number of minimum possible complex roots of the equation

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Reason: The equation

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has maximum four real roots.

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with real coefficients cannot have more than

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