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Question
The roots of the equation x2 + 6x – 4 = 0 are α, β. Find the quadratic equation whose roots are `2/alpha` and `2/beta`
Solution
If the roots are given, the quadratic equation is x2 – (sum of the roots)x + product the roots = 0.
For the given equation.
x2 + 6x – 4 = 0
α + β = – 6
αβ = – 4
`2/alpha + 2/beta = (2beta + 2alpha)/(alphabeta)`
= `(2(alpha+beta))/(alphabeta)`
= `(2(- 6))/(- 4)`
= `(- 12)/(- 4)`
=3
`2/alpha + 2/beta = 4/(alphabeta)`
= `4/(- 4)`
= – 1
∴ The required equation is x2 – 3x – 1 = 0.
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