Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively:
Given: Sum of zeroes = α + β = 1/4
Product of zeroes = αβ = – 1
Then, the quadratic polynomial
= x2 – (sum of zeroes)x + product of zeroes
= 
= 
= 
We can consider 4x2 – x – 4 as required quadratic polynomial because it will also satisfy the given conditions.
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