Question

Find a cubic polynomial with sum, sum of the products of its zeroes taken two at a time and product of its zeroes are $\frac{5}{2},-7,-4$ respectively

Answer 1

If $\alpha ,\beta ,y$ are the zeroes of the cubic polynomial then,
$f\left(x\right)=k[x^3-{(\alpha +\beta +\delta )x}^2+(\alpha \beta +\beta \delta +\delta \alpha )x-\alpha \beta \delta ]$
$=k[x^3-\frac{5}{2}{x}^2-7x-(-4\left)\right]$
$f\left(x\right)=k[2x^3-5x^2-14x+8],k>0$