Question

find a cubic polynomial with the sum, some of the product of its zeros taken two at a time and product of its zeros as 2,-7,-14

Answer 1

hey friend !!!
here is the answer of ur question...

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

= x^3 – (α + β + ɣ)x^2 + (αβ+ βɣ + ɣα)x – (αβɣ) = 0
⇒ x^3 – (2)x^2 + ( – 7 )x – ( – 14) = 0
⇒ x^3 – 2x^2 – 7x + 14 = 0

HOPE IT HELPS
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Answer 2

Answer:

A cubic polynomial is the polynomial whose degree is 3 and it has 3 roots. We will use the sum, sum of the products and products given in the question to find the cubic polynomial. sum of products = α+β+γ=−ba, where b is the coefficient of x2 and a is the coefficient of x3.