Question

find the zeroes of polynomial P(x)=(x-2)²-(x+2)²

Answer 1

if x=0 then p(0)=4-4=0

Answer 2

Given,

The polynomial P(x)=(x-2)²-(x+2)² is given.

To find,

The zeroes of the polynomial P(x)=(x-2)²-(x+2)².

Solution,

The zero of the polynomial P(x)=(x-2)²-(x+2)² is 0.

We can simply find the zeroes of the polynomial by equating the polynomial to 0.

P(x)=(x-2)²-(x+2)²

 (x-2)²-(x+2)² = 0

Transposing (x+2)² to the right of the equal sign, we get

     (x-2)² =( x+2)²

Using (a-b)² = a²+b²-2ab

and    (a+b)² = a²+b²+2ab

(x²+4-4x) = (x²+4+4x)

     -8x = 0

        x =0

Hence, the zero of the polynomial P(x)=(x-2)²-(x+2)² is 0.