Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively. 4,1

Let α and β are the zeroes of the polynomial ax² + bx + c, then we have
α + β = 4 = 4/1 = (-b)/a
αβ = 1 = 1/1 = c/a
On comparing,
a = 1, b= – 4 and c = 1
Hence, the required quadratic polynomial is x² – 4x + 1.

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