Question

If α and β are the roots of the quadratic equation `x^2 - 4x - 6 = 0`, find  the values of (i) `α^2+β^2` (ii) `α^3+β^3`

 

Answer 1

α and β are the roots of` x^2 - 4x - 6 = 0` 

∴` a=1, b=-4,c=-6` α+

`α+β=c/a-6/1=-6` 

`α+β=-b/a=(-(-4))/1=4/1=4` 

`αβ=c/a=-6/1=-6` 

`α^2+β^2=(α+β)^2-2αβ` 

               =`(4)^2-2(-6)` 

              =16+12

              =28 

`  α^3+β^3 =(α+β)^3-3αβ(α+β)`

                 =(4)^3-3(-6)(4)

                  =64+72

                  =136