Question

how to find a quadratic polynomial from the given zeroes 0, -1

Answer 1

We are Given, Zeroes are 0 and -1

so, Polynomial is (x-0)(x+1)
                           = x^2 + x

Answer 2

there is a formula for that.
consider one of the zeroes as α and the other β
let,
α=0 and β= -1
sum of zeroes= α+β
                            =0+-1
                            =-1
product of zeroes=αβ
                              =0×-1
                              =0
then the formula is:
x²-(α+β)x+αβ
x²-(-1)x+0
x²+x
∴the quadratic equation is x²+x