Check whether 3 and -2 are the zeroes of the polynomial when p(x) = x² – x - 6

A zero or root of a polynomial function is a number that, when plugged in for the variable, makes the function equal to zero.

Now,

P(x) = x² – x – 6

Therefore,

P(-2) = (-2)² – (-2) – 6

⇒ P(-2) = 4 + 2 – 6

⇒ P(-2) = 0

P(3) = 3² – 3 – 6

⇒ P(3) = 9 – 3 – 6

-⇒ P(3) = 0

Hence, Yes, 3 and -2 are zeroes of the polynomial x² – x – 6.