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05/07/2021 10:41 am
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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
(iv) p(x) = lx + m, x = −m/l
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05/07/2021 10:45 am
(i) For, x = 1, −1;
p(x) = x2−1
∴p(1) = 12−1 = 1−1 = 0
p(−1) = (-1)2−1 = 1−1 = 0
∴ 1, −1 are zeros of p(x).
(ii) For, x = −1, 2;
p(x) = (x+1)(x–2)
∴ p(−1) = (−1+1)(−1–2)
= (0)(−3) = 0
p(2) = (2+1)(2–2) = (3)(0) = 0
∴ −1, 2 are zeros of p(x).
(iii) For, x = 0 p(x) = x2
p(0) = 02 = 0
∴ 0 is a zero of p(x).
(iv) For, x = -m/l ; p(x) = lx + m
∴ p(-m/l) = l(-m/l)+m = −m + m = 0
∴ -m/l is a zero of p(x).