In the following, determine whether the given values of x are zeroes ofthe given polynomial or not: 6x ²- x - 2; x = -1/2 , x = 2/3

Let p(x) = 6x ² - x -2

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

So, on putting x = -1/2 in the above equation, we get:

p(-1/2) = 6(-1/2) ² - (-1/2) - 2

= 6(1/4) + (1/2) - 2

= (3/2) + (1/2) – 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) = 6(2/3) ² - (2/3) - 2

= 6(4/9) - (2/3) - 2

= (4/3) - (2/3) – 2

= 2/3 – 2

= -(4/3).

Therefore the given value of x is not a zero of the given polynomial.
Therefore the given value of x = -1/2 is a zero and x = 2/3 is not the zero of the given polynomial.