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Find the quadratic polynomial, the sum of whose zeros is and their product is 1. Hence, find the zeros of the polynomial.

Let the zero of the polynomial be α and β

According to the question:

αβ = 1

∴f(x)= x^{2} – (α + β)x + (αβ)

∴ required polynomial f(x)

Put f(x) = 0

x^{2} –(5/2)x + 1= 0

2x^{2} – 5x + 2 = 0

2x^{2} – 4x – x + 2 = 0

2x(x – 2) – 1(x - 2) =0

(x - 2)(2x - 1) = 0

x = 2 or x = 1/2

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