Question

If c is a zero of the polynomial p, which of the following statements must be true?

1) c is a root of the polynomial p
2) c is a factor of the polynomial p
3) is an irrational number
4) c is a positive number

Answer 1

If c is a zero of the polynomial p, it must be true that c is a root of p, and (x - c) could be a factor of p's factored form. However, there's no requirement for c to be irrational or positive.

Step-by-step explanation:

If c is a zero of the polynomial p, the following statements could be true:

1. c is a root of the polynomial p.
2. c could be a factor of the polynomial p, if you're referring to the factor (x - c) being part of the polynomial's factored form.

However, the other options given are not necessarily true:

• Whether c is an irrational number cannot be determined just by knowing it is a zero of the polynomial.
• There is no requirement for c to be a positive number; polynomial zeros can be positive, negative, or even complex numbers.

The general form of a quadratic equation is ax^2 + bx + c = 0, where the solutions can be found using the quadratic formula, but this does not inherently define the nature of the solutions regarding their rationality or sign.