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(iv) p(x) = (x + 1) (x – 2), x = – 1, 2
(v) p(x)
(vi) p(x)
(vii) p(x) =
(viii) p(x)
Asked by Arun Last Modified
Answer 
Tasneem
(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 , then
should 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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