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

## Solution :

Let the cubic polynomial be $$ax^3 + bx^2 + cx + d$$, and its zeroes be $$\alpha$$, $$\beta$$ and $$\gamma$$.

Then,  $$\alpha$$ + $$\beta$$ + $$\gamma$$ = 2 = $$-(-2)\over 1$$ = $$-b\over a$$

$$\alpha$$$$\beta$$ + $$\beta$$$$\gamma$$ + $$\gamma$$$$\alpha$$ = – 7 = $$-7\over 1$$ = $$c\over a$$

and $$\alpha$$$$\beta$$$$\gamma$$ = -14 = $$-14\over 1$$ = $$-d\over a$$

If a = 1, then b = -2, c = -7 and d = 14.

So, one cubic polynomial which satisfy the given conditions will be $$x^3 – 7x + 14$$.