The roots of the equation ax^2+ bx+c=0 are alpha and beta. Form the equation whose roots are ( alpha+1/ beta) and ( beta+ 1/ alpha)
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ax2+bx+c=0
α+β=−ba
α∗β=ca
α+1β=α∗β+1β
β+1α=α∗β+1α
Sum of Roots:
αβ+1β+αβ+1α
=β[αβ+1]+α[αβ+1]αβ
=(α+β)(αβ+1)αβ
=−b/a(c/a+1)c/a
=−bc−ab/a2)c/a
=−bc−abac
Product of Roots:
αβ+1β∗αβ+1α
=αβ+12αβ
=c/a+12αβ
=[c+a]2/a2αβ
=[c2+b2+2ca]/a2c/a
=[a2+c2+2ac]/ac
p(x)=x2−(sum of roots)x+product of roots
=x2+[bc+ab]xac+[a2+c2+2ac]ac
=acx2+[bc+ab]x+[a2+c2+2ca]
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