Question

if alpha and beta are zeroes of polynomial 6x2+x-1,then find the value of
1.alpha cube beta+alpha beta cube
2.alpha/beta+beta/alpha+2(1/alpha+1/beta)+3alpha beta

Answer 1

Answer:  i) -13/216

               ii) -2/3

Step-by-step explanation:

p(x) = 6x²+x-1

Let the zeroes be α & β

α+β = -coefficient of x ÷ coefficient of x² = -1/6

αβ  =  constant term ÷ coefficient of x²  = -1/6

1} α³β+αβ³  = αβ (α²+β²)

                  = αβ { (α+β)²- 2αβ }

on putting the values ,

                =-1/6 { (-1/6)² -2×(-1/6)}

                 =-1/6 { 1/36 + 2/6 }

                   = -1/6 (13/36)

                     = -13/36     ...... Ans

2)    α/β + β/α +2{1/α + 1/β } +3αβ

     =(α²+β²)/αβ + 2 { (α+β)/αβ } + 3αβ

on putting the values.....

      = {(-1/6)²- 2(-1/6)} / -1/6 + 2 {(-1/6)/(-1/6)} +3×(-1/6)

       = -13/6 + 2 - 1/2

        = (-13 +12 - 3) / 6

        =  -4/6

        =   -2/3 .................. Ans

PLEASE MARK IT BRAINLIEST .......

Answer 2

Step-by-step explanation:

solve next by value putting