Question

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

Answer 1

Solution: 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