Determine whether the given values of x are zeroes of the given polynomialor not: x ²+ 6x + 5; x = -1, x = -5.

Let p(x) = x ² + 6x + 5

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 + 6(-1) + 5

= 1 – 6 + 5

= 0.

Therefore the given value of x is a zero of the given polynomial.
If x = -5 is a zero of the polynomial p(x), then it must satisfy p(-5) = 0.

So, on putting x = -5 in the above equation, we get:

p(-5) = (-5) ² + 6(-5) + 5

= 25 – 30 + 5

= 30 – 30

= 0.

Therefore the given value of x is a zero of the given polynomial.