Verify whether the following are zeroes of the polynomial, indicated against them. (i) p(x) = 3x^2 - 1, x = - 1/√3, 2/√3 (ii) p(x) = 2x + 1, x = 1/2
Verify whether the following are zeroes of the polynomial, indicated against them.
(i) p(x) = 3x2 - 1, x = - 1/√3, 2/√3
(ii) p(x) = 2x + 1, x = 1/2
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(i) If x = -1/√3 and x = 2/√3 are zeroes of polynomial p(x) = 3x2 − 1, then
p(-1/√3) and p(2/√3) should be 0.
Here, p(-1/√3) = 3(-1/√3)2 - 1
= 1 - 1 = 0,and
p(2/√3) = 3(2/√3)2 - 1
= 3(4/3) - 1 = 4 - 1 = 3
Hence, x = -1/√3 is a zero of the given polynomial. However, x = 2/√3 is not a zero of the given polynomial.
(ii) If x = 1/2 is a zero of polynomial p(x) = 2x + 1, then p(1/2) should be .
Here, p(1/2) = 2(1/2) + 1 = 1 + 1 = 2
As p(1/2) ≠ 0
Therefore, x = 1/2 is not a zero of the given polynomial.
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