Verify whether the following are zeroes of the polynomial, indicated a

1.	Verify whether the following are zeroes of the polynomial, indicated against them.(i) p(x) = x2 − 1, x = 1, − 1(ii) p(x) = (x + 1) (x − 2), x = − 1, 2(iii) p(x) = x2 , x = 0
Answer» (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.

Verify whether the following are zeroes of the polynomial, indicated against them.(i) p(x) = x2 − 1, x = 1, − 1(ii) p(x) = (x + 1) (x − 2), x = − 1, 2(iii) p(x) = x2 , x = 0

Answer»

(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.