If alpha beta are roots of the polynomial f(x) = x2-px+q then Find value of
1) alpha2 + beta2
2) 1/alpha + 1/beta
3) alpha/beta + beta/alpha
Given quadratic x2 - px + q
Sum of roots = α+β = p
Product of roots = αβ = q
1) (α+β)2 = α2 + β2 + 2αβ
α2 + β2 = (α+β)2 - 2αβ
α2 + β2 = p2 - 2q
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2) 1/α + 1/β = (α + β) / αβ
1/α + 1/β = p / q
-
3)β/α + α/β = (α2 + β2) / αβ
We have proved above
α2 + β2 = p2 - 2q
β/α + α/β = (p2 - 2q )/q
β/α + α/β = p2/q - 2