Determine whether the given values of x are zeroes of the given polynomialor not:
9x ²-3x-2; x = -1/3 , x = 2/3

Let p(x) = 9x ² -3x-2
If x = -1/3 is a zero of the polynomial p(x), then it must satisfy p(-1/3) = 0.

So, on putting x = -1/3 in the above equation, we get:

p(-1/3) = 9(-1/3) ² - 3(-1/3) - 2

= 1 + 1 - 2

= 2 – 2

= 0.

Therefore the given value of x is a zero of the given polynomial.
If x = 2/3 is a zero of the polynomial p(x), then it must satisfy p(2/3) = 0.

So, on putting x = 2/3 in the above equation, we get:

p(2/3) = 9(2/3) ² - 3(2/3) - 2

= 4 - 2 - 2

= 4 – 4

= 0.

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