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Question
Verify whether the following zeroes of the polynomial, indicated against them.
p(x) = 3x2 – 1, x = `-1/sqrt3,2/sqrt3`
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Solution
If `x = -1/sqrt3` and `x = 2/sqrt3` are zeroes of polynomial p(x) = 3x2 − 1, then `p(-1/sqrt3)` and `p(2/sqrt3)` should be 0.
Here, `p(-1/sqrt3)=3(-1/sqrt3)^2-1=3(1/3)-1=1-1=0,`
Also, `p(2/sqrt3)=3(2/sqrt3)^2-1=3(4/3)-1=4-1=3`
Hence, `x=-1/sqrt3` is a zero of the given polynomial.
However, `x=2/sqrt3` is not a zero of the given polynomial.
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