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Question
Find the condition that one of the roots of ax2 + bx + c may be reciprocal of the other
Solution
The given quadratic equation is
ax2 + bx + c = 0 ......(1)
Let α and β be the roots of the equation (1) then
Sum of the roots α + β = 0 ......(2)
Product of the roots αβ = 0 ......(3)
One root is reciprocal of the other
β = `1/α`
(2) ⇒ `α + 1/α = - "b"/"a"`
(3) ⇒ `α xx 1/α = "c"/"a"`
1 = `"c"/"a"`
c = a
When is the required condition?
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