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)= x2 – (α + β)x + (αβ)



∴ required polynomial f(x)


Put f(x) = 0


x2 –(5/2)x + 1= 0


2x2 – 5x + 2 = 0


2x2 – 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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