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Find the zeroes of the polynomial $f(x)=2 \sqrt{3} x^{2}-5 x+\sqrt{3}$ and verify the relation between its zeroes and coefficients.
Find the zeroes of the polynomial $f(x)=2 \sqrt{3} x^{2}-5 x+\sqrt{3}$ and verify the relation between its zeroes and coefficients.
CBSE | Class 10 | Excercise 2A | Maths | Polynomials | RS Aggarwal
Find the zeroes of the polynomial $f(x)=2 \sqrt{3} x^{2}-5 x+\sqrt{3}$ and verify the relation between its zeroes and coefficients.

$$
\begin{aligned}
&2 \sqrt{3} x^{2}-5 x+\sqrt{3} \\
&\Rightarrow 2 \sqrt{3} x^{2}-2 x-3 x+\sqrt{3} \\
&\Rightarrow 2 x(\sqrt{3} x-1)-\sqrt{3}(\sqrt{3} x-1)=0 \\
&\Rightarrow(\sqrt{3} x-1) \text { or }(2 x-\sqrt{3})=0 \\
& & \Rightarrow(\sqrt{3} x-1)=0 \text { or }(2 x-\sqrt{3})=0 \\
& & \Rightarrow x=\frac{1}{\sqrt{3}} \text { or } x=\frac{\sqrt{3}}{2} \\
&\Rightarrow x=\frac{1}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}}=\frac{\sqrt{3}}{3} \text { or } x=\frac{\sqrt{3}}{2}
\end{aligned}
$$

Sum of zeroes $=\frac{\sqrt{3}}{3}+\frac{\sqrt{3}}{2}=\frac{5 \sqrt{3}}{6}=\frac{-(\text { coefficient of } x)}{\left(\text { coefficient of } x^{2}\right)}$

Product of zeroes $=\frac{\sqrt{3}}{3} \times \frac{\sqrt{3}}{2}=\frac{\sqrt{3}}{6}=\frac{\text { constant term }}{\left.\text { (coefficient of } x^{2}\right)}$

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