Find the number of zeros of the following polynomials:

p(x) = x —x² —1

Here, p(x) = x —x² —1

To find the zeros of p(x), consider p(x) = 0

∴ x – x² – 1 = 0

Taking negative common

x² – x + 1 = 0

x² – x + + 1 – = 0

(Adding and subtracting in order to do factorization)

+ = 0

Using the identity: (a– b) ² = (a² – 2ab + b²)

= –

The above equation cannot be true as the square of a real number cannot be negative.

⇒ No zero exists for p(x).

Hence, the number of zeros of the given polynomial is 0.