Find a cubic polynomial with the sum of its zeros, sum of the product of its zeros taken two at a time and product of its zeros as 2, -7, - 14 respectively.

Let, $\alpha ,\beta ,\gamma$ be the zeros of the given cubic polynomial. Then, we have
$\alpha +\beta +\gamma =2$
$\alpha \beta +\beta \gamma +\gamma \alpha =-7$
$\alpha \beta \gamma =-14$
Now, the required polynomial$=k\times [x^3-(\alpha +\beta +\gamma )x^2+(\alpha \beta +\beta \gamma +\gamma \alpha )x-(\alpha \beta \gamma )]$, where k is real constant.
                                                 $=k\times [x^3-2x^2+(-7)x-(-14)]$
                                                 $=k\times (x^3-2x^2-7x+14)$