# 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.

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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.

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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