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