Question

form a cubic polynomial whose zeros are 3,-root3, root 3

Answer 1

Let α,β and γ be the zeroes.

α=3
β=-√3
γ=√3

Sum of zeroes = α+β+γ=3+(-√3)+√3
=3-√3+√3
=3

Sum of the product of zeroes taken two at a time
=αβ+βγ+αγ
=3(-√3)+(√3)(-√3)+3(√3)
=-3√3-3+3√3
= -3

Product of all zeroes =αβγ
=(3)(-√3)(√3)
=3(-3)
= -9

A cubic polynomial which has three zeroes is in the form of
x³-(α+β+γ)x²+(αβ+βγ+αγ)x-αβγ

⇒x³-3x²+(-3)x-(-9)
⇒x³-3x²-3x+9

Hope it helps

Answer 2

Hi there !

 α , β and γ  are the  zeroes of the cubic polynomial

α = 3  ,   β = -√3  ,  γ = √3

Sum of zeroes = α + β + γ
                          = 3+ (-√3)+√3
                          = 3

Sum of the product of zeroes  [taken two at a time ]  = αβ + βγ + αγ
                                                                 =3(-√3)+(√3)(-√3)+3(√3)
                                                                 =  -3√3 - 3 + 3√3
                                                                 = -3

Product of all zeroes  =  αβγ
                                  = 3 × -√3 × √3
                                  = -9

A cubic polynomial  :- 

x³ - ( sum of zeroes )x²+( sum of zeroes taken two at a time )x- [ product of zeroes ]

 =  x³- 3x²+ (-3)x-(-9)
 
=  x³-3x²-3x+9               ------> required polynomial