(i) If x = 1 and x = −1 are zeroes of polynomial p(x) = x2 − 1, then p(1) and p(−1) should be 0.
Here, p(1) = (1)2 − 1 = 0, and
p(− 1) = (− 1)2 − 1 = 0
(ii) If x = −1 and x = 2 are zeroes of polynomial p(x) = (x +1) (x − 2), then p(−1) and p(2)should be 0.
Here, p(−1) = (− 1 + 1) (− 1 − 2) = 0 (−3) = 0, and
p(2) = (2 + 1) (2 − 2 ) = 3 (0) = 0
(iii) If x = 0 is a zero of polynomial p(x) = x2, then p(0) should be zero. Here, p(0) = (0)2 = 0
Hence, x = 0 is a zero of the given polynomial.