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प्रश्न
If α, β are the zeroes of the polynomial f(x) = 5x2 – 7x + 1 then `1/α + 1/β = ?`
If α and β are the zeroes of the polynomial f(x) = 5x2 – 7x + 1, find the value of `(1/α + 1/β)`.
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उत्तर
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 = (-(-7))/5` and `αβ = 1/5`
⇒ `α + β = 7/5` and `αβ = 1/5`
Now, `1/α + 1/β = (α + β)/(αβ)`
= `(7/5)/(1/5)`
= 7
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