One zero of f(x)=2x^3−x^2−2x+1 is -1. What are the other zeros of the function?

Answer 1

To find the other zeros of the function, we can use polynomial long division or synthetic division.

Using synthetic division, we divide the polynomial f(x) = 2x^3 - x^2 - 2x + 1 by x + 1.

-1 | 2 -1 -2 1
-2 3 -1
-----------------
2 -3 1 0

The result of the division is 2x^2 - 3x +1.

Now, we factor the quadratic polynomial:
2x^2 - 3x + 1 = (2x - 1)(x - 1).

Setting each factor equal to zero, we have:
2x - 1 = 0, which gives x = 1/2.
x - 1 = 0, which gives x = 1.

Therefore, the other zeros of the function are x = 1/2 and x = 1.