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Question:

Find the zero of the polynomial in each of the following cases:
(i) p(x) = x + 5
(ii) p(x) = x - 5
(iii) p(x) = 2x + 5
(iv) p(x) = 3x - 6
(v) p(x) = 3x
(vi) p(x) = ax, a ≠ 0
(vii) p(x) = cx + d, c ≠ 0, c, d are real numbers.

Solution:

To find the zero of the polynomial, p(x) = 0
(i) If p(x) = x + 5 = 0, then x = -5, i.e., -5 is the zero
(ii) If p(x) = x - 5 = 0, then x = 5, i.e., 5 is the zero
(iii) If p(x) = 2x + 5 = 0, then x = -5/2, i.e., -5/2 is the zero
(iv) If p(x) = 3x - 6 = 0, then x = 2, i.e., 2 is the zero
(v) If p(x) = 3x = 0, then x = 0, i.e., 0 is the zero
(vi) If p(x) = ax = 0, then x = 0, i.e., 0 is the zero
(vii) If p(x) = cx + d = 0, then x = -d/c, i.e., -d/c is the zero.