Question

Form a cubic polynomial with sum, product and sum of products of it's zeroes taken two at a time as 2,-7,-14 respectively

Answer 1

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

which are bold that are powers of polynomials

Answer 2

Hii !!!


Given: a,b ,c are roots or zeros of the polynomial.
           a+b+c        = 2
           ab+bc+ca  = -7
           abc            = -14

p(x) = k[x cube - (a+b+c)x square + (ab+bc+ca )x - abc]
f(x)  = k[x cube - 2x square-7x+14]


Here 
 a = alpha
 b = beta
 c = gama
cube = power 3
square = power 2

I hope this will help you .
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