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