Question

The zeroes of the polynomial, 3x 2 -1 are

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{Polynomial is}\;\mathsf{3\,x^2-1}$

$\underline{\textbf{To find:}}$

$\textsf{Zeroes of the polynomial}\;\mathsf{3\,x^2-1}$

$\underline{\textbf{Solution:}}$

$\mathsf{Let\;f(x)=3\,x^2-1}$

$\textsf{This can be written as,}$

$\mathsf{f(x)=(\sqrt{3}\,x)^2-1^2}$

$\textsf{Using the identity,}\;\boxed{\bf\,a^2-b^2=(a-b)(a+b)}$

$\mathsf{f(x)=(\sqrt{3}\,x-1)\,(\sqrt{3}\,x+1)}$

$\mathsf{f(x)=0\;\implies}$

$\implies\mathsf{(\sqrt{3}\,x-1)\,(\sqrt{3}\,x+1)=0}$

$\implies\mathsf{\sqrt{3}\,x-1=0\;\;(or)\;\;\sqrt{3}\,x+1=0}$

$\implies\mathsf{\sqrt{3}\,x=1\;\;(or)\;\;\sqrt{3}\,x=-1}$

$\implies\mathsf{x=\dfrac{1}{\sqrt3}\;\;(or)\;\;x=\dfrac{-1}{\sqrt3}}$

$\therefore\textbf{Zeroes of the polynomial are}\;\mathsf{\dfrac{1}{\sqrt3}\;and\;\dfrac{-1}{\sqrt3}}$

Answer 2

Zeroes of the given polynomial$3x 2 -1$  are$\frac{1}{\sqrt{3}} and \frac{-1}{\sqrt{3}}$

Polynomial

Polynomials are algebraic expressions that consist of variables and coefficients.

Solution:

Given $f(x)=3 x^{2}-1$

This can be written as,

$f(x)=(\sqrt{3} x)^{2}-1^{2}$

Using the identity, $\mathbf{a}^{2}-\mathbf{b}^{2}=(\mathbf{a}-\mathbf{b})(\mathbf{a}+\mathbf{b})$

$f(x)=(\sqrt{3} x-1)(\sqrt{3} x+1)$

$f(x)=0$

$\Longrightarrow(\sqrt{3} x-1)(\sqrt{3} x+1)=0$

$\Longrightarrow \sqrt{3} x-1=0 \text { (or) } \sqrt{3} x+1=0$

$\Longrightarrow \sqrt{3} x=1 \text { (or) } \sqrt{3} x=-1$

$\Longrightarrow x=\frac{1}{\sqrt{3}} \text { (or) } x=\frac{-1}{\sqrt{3}}$

Hence the  zeroes of the polynomial are$\frac{1}{\sqrt{3}} and \frac{-1}{\sqrt{3}}$

learn more about roots of a polynomial here

https://brainly.in/question/4792957?msp_poc_exp=4

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