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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`
Solution
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
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