Question

find the quadratic polynomial ,the sum of whose zeros is 0 and their product is -1 . Hence ,find the zeros of the polynomial

Answer 1

Here, let the zeros be a and b. The required quadratic equation is of the form
x^2-(a+b)x+a.b
Sum of zeros =0
Product of zeros =-1
The polynomial is x^2-1
x^2-1=(x+1)(x-1)
The zeros are +1 and -1

Answer 2

Let S be the sum of the roots and P be the product of the roots for any polynomial ax^2+ bx + c.
Then,
Polynomial = x^2 + (S)x + (P)
                  = x^2 + (0)x + (-1)
                  = x^2 -1
roots = x^2 - 1 = 0
         = (x+1)(x-1) = 0
         
x = +1 , -1
Plz mark it as the BRAINLIEST.