Let , , and be the roots of the equation . If , , then which of the following are…

MATHEMATICS · Multi correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Let

\alpha

\beta

, and

\gamma

be the roots of the equation

x^3-4x+1=0

. If

T_n=\alpha^n+\beta^n+\gamma^n

n\geq1

, then which of the following are true?

[x]

denotes the greatest integer less than or equal to

x

. (A)

T_6-4T_4=3

(B)

T_{96}+2T_{99}+T_{102}=16T_{98}

(C)

T_{96}+2T_{99}+T_{102}=16T_{100}

(D)

[\alpha]+[\beta]+[\gamma]=2