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Question
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.
`0, sqrt5`
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Solution
Given: α + β = 0, αβ = `sqrt5`
Since ax2 + bx + c = k[x2 - (α + β)x + αβ]
Or `(ax^2 + bx + c)/k = (x^2 - 0x + sqrt5)`
or `(ax^2 + bx + c)/k = (x^2 + sqrt5)/1`
Here k is a constant term, by comparing k = 1
Hence, ax2 + bx + c = `x^2 + sqrt5`
The quadratic polynomial is `x^2 + sqrt5`.
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