(Q3)Find a cubic polyomial with the sum, sum of the product of its zeros taken two at a time, and the product of its zeros as 2, -7, -14 respectively

Answer:

Let the cubic polynomial be ax3+bx2+cx+d, and its zeros be α,β and γ

Then

α+β+γ =
-(-)
1
 =
-b
a
αβ+βγ+γα= - =
-
1
 =
c
a
αβγ = -=
-
1
 =
-d
a

a= then b= - and c= -and d=

So, one cubic polynomial which satisfies the given conditions will be x3 - 2x2 - 7x+14