The zeros of the polynomial p(x) = 3x2

Foundation

Mathematics Foundation

zeros of a polynomial

Question

The zeros of the polynomial p(x) = 3x² – 1 are

$\frac{1}{\sqrt{3}} and \sqrt{3}$

$\frac{- 1}{\sqrt{3}} and \sqrt{3}$

$\frac{1}{3} and 3$

$\frac{1}{\sqrt{3}} and \frac{- 1}{\sqrt{3}}$

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To find the zeros of the polynomial p(x) = 3x² – 1, we set it equal to zero and solve for x:

3x² − 1 = 0

Add 1 to both sides: 3x² = 1

Divide both sides by 3: $x^{2} = \frac{1}{3}$

Take the square root of both sides: $x = \pm \sqrt{\frac{1}{3}} = \pm \frac{1}{\sqrt{3}}$

Therefore, the zeros are $\frac{1}{\sqrt{3}}$ and $\frac{- 1}{\sqrt{3}}$ .

Final Answer: $\frac{1}{\sqrt{3}} and \frac{- 1}{\sqrt{3}}$