Question

find a cubic polynomial with sum of its zeros sum of the product of the zeros when taken two together and product of its zeroes as 2 ,- 7 and - 14 respectively​

Answer 1

Step-by-step explanation:

Let α, β and ɣ be the roots of the cubic polynomial

Given (α + β + ɣ) = 2

(αβ+ βɣ + ɣα) = – 7 and (αβɣ) = –14

The cubic polynomial with roots α, β and ɣ is x3 – (α + β + ɣ)x2 + (αβ+ βɣ + ɣα)x – (αβɣ) = 0

⇒ x3 – (2)x2 + ( – 7 )x – ( – 14) = 0

⇒ x3 – 2x2 – 7x + 14 = 0