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[Solved] 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

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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) For, x = -1/√3 , 2/√3 ; p(x) = 3x2−1

∴p(-1/√3) = 3(-1/√3)2-1

= 3(1/3)-1 = 1-1 = 0

∴p(2/√3 ) = 3(2/√3)2-1 = 3(4/3)-1

= 4−1=3 ≠ 0

∴-1/√3 is a zero of p(x) but 2/√3  is not a zero of p(x).

(ii) For, x = 1/2 p(x) = 2x+1

∴ p(1/2) = 2(1/2) + 1

= 1 + 1 = 2≠0

∴1/2 is not a zero of p(x).

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