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Find the zeroes of the quadratic polynomial $\left(3 x^{2}-x-4\right)$ and verify the relation between the zeroes and the coefficients.
Find the zeroes of the quadratic polynomial $\left(3 x^{2}-x-4\right)$ and verify the relation between the zeroes and the coefficients.
CBSE | Class 10 | Excercise 2A | Maths | Polynomials | RS Aggarwal
Find the zeroes of the quadratic polynomial $\left(3 x^{2}-x-4\right)$ and verify the relation between the zeroes and the coefficients.

$$
\begin{aligned}
&3 x^{2}-x-4=0 \\
&\Rightarrow 3 x^{2}-4 x+3 x-4=0 \\
&\Rightarrow x(3 x-4)+1(3 x-4)=0 \\
&\Rightarrow(3 x-4)(x+1)=0 \\
&\Rightarrow(3 x-4) \text { or }(x+1)=0 \\
&\Rightarrow x=\frac{4}{3} \text { or } x=-1
\end{aligned}
$$

Sum of zeroes $=\frac{4}{3}+(-1)=\frac{1}{3}=\frac{-(\text { coefficient of } x)}{\left(\text { coef ficient of } x^{2}\right)}$

Product of zeroes $=\frac{4}{3} \times(-1)=\frac{-4}{3}=\frac{\text { constant term }}{\left(\text { coefficient of } x^{2}\right)}$

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