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Also, product $\newline$$P$ of zeroes $\newline$$\frac{\alpha-1}{\alpha+1}\times\frac{\beta-1}{\beta+1}=\frac{1}{(\alpha+1)(\beta+1)}$$\newline$$=\frac{\alpha \beta-\alpha-\beta+1}{\alpha \beta+\alpha+\beta+1}=\frac{\alpha \beta-(\alpha+\beta)+1}{\alpha \beta+(\alpha+\beta)+1}=\frac{3-2+1}{3+2+1}=\frac{2}{6}=\frac{1}{3}$$\newline$:. Required quadratic polynomial, $\newline$$p(x)=k{x^{2}-Sx+P}$$\newline$$\Rightarrow p(x)=k{x^{2}-\frac{2}{3}x+\frac{1}{3}}$. Example $32$ : If the product of the zeroes of the quadratic polynomial $\newline$$p(x)=ax^{2}-6x-6$ is $4$, then find the value of $\newline$$a$. Also, find the sum of the zeroes of the polynomial.$\newline$Solution : We have, $\newline$$*p(x)=ax^{2}-6x-6$. It is given that : $\newline$$\alpha \beta=4$$\newline$Let $\newline$$\frac{\alpha-1}{\alpha+1}\times\frac{\beta-1}{\beta+1}=\frac{1}{(\alpha+1)(\beta+1)}$$0$ be the zeroes of the polynomial.