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)= x^{2} – (α + β)x + (αβ)

=x^{2} - 0x - 1

∴required polynomial f(x) = x^{2} - 1

Put f(x) = 0

x^{2} - 1 = 0

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

x = 1 or x = -1

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