Which of the following properly describes the relationship between the degree of a polynomial and the number of zeros it has?(1 point)
The degree of the polynomial is the greatest number of zeros the polynomial could have.
The degree of the polynomial is the least number of zeros the polynomial could have.
The degree of the polynomial is double the number of zeros.
The degree of the polynomial is half the number of zeros.
The correct answer is: The degree of the polynomial is the least number of zeros the polynomial could have.
To understand why this is the case, let's first define the degree of a polynomial. The degree of a polynomial is the highest exponent of its variable. For example, in the polynomial 3x^2 + 2x - 5, the degree is 2 because the highest exponent of x is 2.
Now, let's consider the relationship between the degree of a polynomial and the number of zeros it has. The zeros of a polynomial are the values of the variable that make the polynomial equal to zero. For example, in the polynomial 3x^2 + 2x - 5, the zeros are the values of x that satisfy the equation 3x^2 + 2x - 5 = 0.
The fundamental theorem of algebra states that a polynomial of degree n has exactly n zeros, including both real and complex zeros. So, if a polynomial has a degree of 2, it will have at least 2 zeros. However, it is important to note that a polynomial can have more zeros than its degree, but it cannot have fewer.
Therefore, out of the given options, the correct answer is that the degree of the polynomial is the least number of zeros the polynomial could have.
The correct answer is:
The degree of the polynomial is the greatest number of zeros the polynomial could have.