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Question

# Verify whether the following are zeroes of the polynomial, indicated against them. (i) (ii) (iii) p(x) = x2 − 1, x = 1, − 1 (iv) p(x) = (x + 1) (x − 2), x = − 1, 2 (v) p(x) = x2 , x = 0 (vi) p(x) = lx + m (vii) (viii)

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Solution

## (i) If is a zero of given polynomial p(x) = 3x + 1, then should be 0. Therefore, is a zero of the given polynomial. (ii) If is a zero of polynomial p(x) = 5x − π , thenshould be 0. Therefore, is not a zero of the given polynomial. (iii) 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 Hence, x = 1 and −1 are zeroes of the given polynomial. (iv) 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 Therefore, x = −1 and x = 2 are zeroes of the given polynomial. (v) 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. (vi) If is a zero of polynomial p(x) = lx + m, then should be 0. Here, Therefore, is a zero of the given polynomial. (vii) If and are zeroes of polynomial p(x) = 3x2 − 1, then Hence, is a zero of the given polynomial. However, is not a zero of the given polynomial. (viii) If is a zero of polynomial p(x) = 2x + 1, then should be 0. Therefore, is not a zero of the given polynomial.

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