Q17 of 113 Page 50

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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