Answer:

To check whether 3/2 and -2/3 are the zeroes of the polynomial P(x) = 6x^2 - 5x - 6, you can substitute these values into the polynomial and see if they result in zero.

For x = 3/2:

P(3/2) = 6(3/2)^2 - 5(3/2) - 6

P(3/2) = 6(9/4) - 15/2 - 6

P(3/2) = 54/4 - 15/2 - 6

P(3/2) = 27/2 - 15/2 - 6

P(3/2) = (27 - 15 - 12)/2

P(3/2) = 0/2

P(3/2) = 0

For x = -2/3:

P(-2/3) = 6(-2/3)^2 - 5(-2/3) - 6

P(-2/3) = 6(4/9) + 10/3 - 6

P(-2/3) = 24/9 + 10/3 - 6

P(-2/3) = (8/3) + (10/3) - 6

P(-2/3) = (8 + 10 - 18)/3

P(-2/3) = 0/3

P(-2/3) = 0

Both P(3/2) and P(-2/3) equal zero, which means that 3/2 and -2/3 are indeed the zeroes of the polynomial P(x) = 6x^2 - 5x - 6.