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Question
If α and β are the zeros of the polynomial f(x) = 6x2 + x – 2, find the value of `(α/β + α/β)`.
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Solution
By using the relationship between the zeroes of the quadratic polynomial.
We have
Sum of zeroes = `(-("Coefficient of" x))/("Coefficient of" x^2)` and Product of zeroes = `"Constant term"/("Coefficient of" x^2)`
∴ `α + β = -1/6` and `αβ = -1/3`
Now, `α/β + β/α = (α^2 + β^2)/(αβ)`
= `(α^2 + β^2 + 2αβ - 2αβ)/(αβ)`
= `((α + β)^2 - 2αβ)/(αβ)`
= `((-1/6)^2 - 2(-1/3))/(-1/3)`
= `(1/36 + 2/3)/(-1/3)`
= `-25/12`
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