Question

# Form a cubic polynomial having sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes are 2, -7 and -14 respectively.

Solution

Let the cubic polynomial be ax3 + bx2 + cx + d ....... (1)
Let a, ß, y be the zeroes of the required cubic polynomial,
then
a+B+y = 5: «B+BY+ ya =-; and aßy =
Now, according to the question, a +B+y=2
-d
a
aß +By+ya=-==-=-7
And apy=-14 --14, -14
Ifa= 1, then b=-2,c=-7, d=14
Substituting the values of a, b, c and d in (i), we get the
required cubic polynomial x3 – 2x2 - 7x + 14
This polynomial satisfies all the given conditions