Zeroes of a Polynomial A zero of a polynomial is a value of the variable for which the polynomial equals zero. In simpler terms, it is a value of x that...
A zero of a polynomial is a value of the variable for which the polynomial equals zero. In simpler terms, it is a value of x that makes the polynomial equal to 0.
Example: Consider the polynomial
For this polynomial to equal 0, we need
Setting each individual coefficient to zero, we get:
Therefore, the zeros of this polynomial are x = 0 and x = -2.
Characteristics of Polynomial Zeroes:
A polynomial with real coefficients will have real zeros.
The number and type of zeros of a polynomial are determined by its degree.
A polynomial with degree 1 or 2 will have exactly one real zero.
A polynomial with degree 3 or higher will have exactly three real zeros (including one multiple zero).
Identifying Polynomial Zeroes:
Look for factors of the leading coefficient of the polynomial.
If the leading coefficient is 1, the polynomial has one factor (x - a), where a is a coefficient in the polynomial.
If the leading coefficient is not 1, the polynomial has more than one factor.
Applications of Polynomial Zeroes:
Polynomial zeros can be used to solve equations that involve polynomials.
They can also be used to graph polynomial functions.
Knowing the zeros of a polynomial can help to factorize it.
Note: The degree of a polynomial is the highest power of the variable in the polynomial