If a and b are to zeroes of quadratic polynomial x2 + 2px+ q find the Vale of 1/alpha +1/beta
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α+ β = -p αβ = q
(1/α + 1/β) = (α + β) / αβ = - p / q
1/αβ = 1 / q.
If 1/α, 1/β are zeros of the quadratic polynomial then the equation is
x2 -(1 / α + 1 / β)x + 1 / αβ = 0 then
x2 -(-p / q)x + 1 / q = 0
qx2 + px + 1 = 0
(1/α + 1/β) = (α + β) / αβ = - p / q
1/αβ = 1 / q.
If 1/α, 1/β are zeros of the quadratic polynomial then the equation is
x2 -(1 / α + 1 / β)x + 1 / αβ = 0 then
x2 -(-p / q)x + 1 / q = 0
qx2 + px + 1 = 0
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hope it was helpful
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