Find a cubic polynomial with the sum, the sum of the product of its zeroes taken two at a time and the product of its zeroes are \(2, -7,-14\) respectively.

The general form of cubic equation is \(ax^3 + bx^2 + cx + d\)

Let the three zeroes be p,q and r
Here:
\(p + q + r\) = \({{-b}\over{a}} = 2\) ............(i)
\(pq + qr + rp\) = \({{c}\over{a}} = -7\)..........(ii)
\(pqr\) = \({{-d}\over{a}} = -14\).................(iii)

On equating (i), (ii) and (iii) => \(a = 1,b = -2,c = -7,d = 14\)

Putting the values of a,b,c and d in general form

=> \(x^3 - 2x^2 - 7x + 14\)