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Question
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.
`-1/4 ,1/4`
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Solution
Given: α + β = `-1/4`, αβ = `1/4`
Since ax2 + bx + c = k[x2 - (α + β)x + αβ]
Or `(ax^2 + bx + c)/k = x^2 - (-1/4x) + 1/4)`
Or `(ax^2 + bx + c)/k = (4x^2 + 4x + 1)/4`
Here k is a constant term, by comparing k = 4
Hence, ax2 + bx + c = `4x^2 + 4x + 1`
The quadratic polynomial is `4x^2 + 4x + 1`.
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