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Verify whether the following zeroes of the polynomial, indicated against them. p(x) = 3x^2 – 1, x = -1/√3, 2/√3 - Mathematics

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ConceptZeroes of a Polynomial

Question

Verify whether the following zeroes of the polynomial, indicated against them.

`p(x) = 3x^2 – 1, x = -1/sqrt3,2/sqrt3`

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," and"`

          `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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Solution Verify whether the following zeroes of the polynomial, indicated against them. p(x) = 3x^2 – 1, x = -1/√3, 2/√3 Concept: Zeroes of a Polynomial.
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