The number of rational roots of equation  x(x + 2)(x2 − 1) − 1  =  0  are/isSelect an answerA0B4C1D2

The given equation is x(x + 2)(x^2 - 1) - 1 = 0.

Let's simplify this equation:

x(x + 2)(x^2 - 1) = 1

x(x^3 - x + 2x - 2) = 1

x^4 - x^2 + 2x^2 - 2x - 1 = 0

x^4 + x^2 - 2x - 1 = 0

This is a quartic equation. The rational root theorem states that any rational root, p/q (where p and q are relatively prime), of a polynomial equation

anx^n + an-1x^n-1 + ... + a2x^2 + a1x + a0 = 0

must be such that p is a factor of a0 and q is a factor of an.

In this case, a0 = -1 and an = 1. The factors of -1 are -1 and 1, and the factor of 1 is 1. Therefore, the possible rational roots of the equation are -1/1, 1/1, which are -1 and 1.

Substituting these values into the equation, we find that neither -1 nor 1 is a root of the equation.

Therefore, the equation has 0 rational roots. So, the correct answer is A0.