Determine whether the given value of x is a zero of the given polynomialor not: x ²+ x + 1; x = -1.

Let p(x) = x ² + x + 1

If x = -1 is a zero of the polynomial p(x), then it must satisfy p(-1) = 0.

So, on putting x = -1 in the above equation, we get:
p(-1) = (-1) ² + (-1) + 1

= 1 – 1 + 1

= 1 ¹ 0.

Therefore the given value of x is not a zero of the given polynomial.