Question

True or False : Polynomials with integer coefficients always have integer zeros.

Answer 1

False. Polynomials with integer coefficients do not always have integer zeros.

Step-by-step explanation:

False. Polynomials with integer coefficients do not always have integer zeros. For example, consider the polynomial f(x) = x^2 - 2. This polynomial has integer coefficients, but its zeros are not integers. The zeros of f(x) are the square root of 2 and the negative square root of 2, which are not integers.

Polynomials are algebraic expressions that consist of variables and coefficients, combined using addition, subtraction, and multiplication. The zeros of a polynomial are the values of the variable that make the polynomial equal to zero. While some polynomials with integer coefficients may have integer zeros, it is not always the case.