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# If α and β Are the Roots of the Quadratic Equation X 2 − 4 X − 6 = 0 , Find the Values of (I) α 2 + β 2 (Ii) α 3 + β 3 - Algebra

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

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#### 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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