Multiple choice

The number of roots of equation (x^{\frac{2}{3}} + x^{\frac{1}{3}} - 2 = 0) is:

  1. 2

  2. 4

  3. 3

  4. 1
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A Correct answer
Explanation

Substitute y = x^(1/3). Then equation becomes y² + y - 2 = 0. Factorizing: (y+2)(y-1) = 0. So y = -2 or y = 1. This gives x = (-2)³ = -8 and x = 1³ = 1. Both satisfy original equation, so there are 2 real roots.

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