nanno na Verify whether the following are zeroes of the polynomial, indicated against them.
Answers
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Answer:
In general, we say that a zero of a polynomial p(x) is a number c such that p(c) = 0.
(i) p(x) = 3x + 1, x = -(1/3)
p(-1/3) = 3 × (-1/3) + 1 = 0
Therefore, -1/3 is a zero of p(x).
(ii) p(x) = 5x - π, x = 4/5
p(4/5) = 5(4/5) - π
We know that, π = 22/7
Thus, p(4/5) = 4 - 22/7 ≠ 0
Therefore, 4/5 is not a zero of p(x).
(iii) p(x) = x2 - 1, x = 1, -1
p(1) = 12 - 1 = 0
p(-1) = (-1)2 - 1 = 1 - 1 = 0
Therefore, 1 and -1 are zeroes of p(x).
(iv) p(x) = (x + 1)(x - 2), x = -1, 2
p(-1) = (-1 + 1)(-1 - 2) = 0 × (-3) = 0
p(2) = (2 + 1)(2 - 2) = 3 × 0 = 0
Therefore, -1 and 2 are zeroes of p(x).
(v) p(x) = x2, x = 0
p(0) = 02 = 0
Therefore, 0 is a zero of p(x).
(vi) p(x) = lx + m, x = -(m/l)
p(-m/l) = l × (-m/l) + m
⇒ -m + m = 0
Therefore, -(m/l) is a zero of p(x).
(vii) p(x) = 3x2 - 1, x = -(1/√3), 2/√3
p(-1/√3) = 3 × (-1/√3)2 - 1
= 3 × (1/3) - 1 = 1 - 1 = 0
Therefore, -1/√3 is a zero of p(x).
p(2/√3) = 3 × (2/√3)2 - 1
= 3 (4/3) - 1
= 4 - 1 = 3 ≠ 0
Therefore, 2/√3 is not a zero p(x).
(viii) p(x) = 2x + 1, x = 1/2
p(1/2) = 2 × (1/2) + 1
= 1 + 1 = 2 ≠ 0
Therefore, 1/2 is not a zero of p(x).