Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. 

(i) $\frac{1}{4}, -1$ (ii) $\sqrt{2}, \frac{1}{3}$ (iii) $0, \sqrt{5}$ (iv) 1, 1 (v) $\frac{-1}{4}, \frac{1}{4}$ (vi) 4, 1

(i)  Given zeros $\frac{1}{4}, -1.$

Sum of the zeroes$=\frac{1}{4}+\left(-1\right)=\frac{-3}{4}.$

Product of the zeroes$=\frac{1}{4}\times \left(-1\right)=\frac{-1}{4}.$

Quadratic equation formula is $x^2-(Sum of zeroes)x+product of zeroes=0.$

$$\begin{gathered} \Rightarrow x^2-\left(\frac{-3}{4}\right)x-\frac{1}{4}=0 \\ \Rightarrow 4x^2+3x-1=0. \end{gathered}$$

Thus, the quadratic polynomial is $4x^2+3x-1=0$