Q16 of 113 Page 50

Find the quadratic polynomial, the sum of whose zeros is 0 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,


α + β = 0


αβ = -1


∴f(x)= x2 – (α + β)x + (αβ)


=x2 - 0x - 1


∴required polynomial f(x) = x2 - 1


Put f(x) = 0


x2 - 1 = 0


(x - 1)(x + 1)=0


x = 1 or x = -1


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