Complex Roots of a Polynomial – Examples and Practice Problems

Complex Roots of a Polynomial – Examples and Practice Problems

The number of roots in a polynomial is equal to the degree of that polynomial. For example, in quadratic polynomials, we will always have two roots counted by multiplicity. These roots could be real or complex depending on the determinant of the quadratic equation....
Complex Conjugate Roots – Examples and Practice Problems

Complex Conjugate Roots – Examples and Practice Problems

The complex conjugate roots of a polynomial are those complex roots that are conjugate to each other. Remember that conjugates are two complex numbers that have the same real part and have the negative part with a different sign from each other. Here, we will look at...
Domain and Range of Logarithmic Functions

Domain and Range of Logarithmic Functions

Logarithmic functions are the inverse functions of the exponential functions. This means that their domain and range are swapped. The domain of logarithmic functions is equal to all real numbers greater or less than the vertical asymptote. The range of exponential...
Domain and Range of Trigonometric Functions

Domain and Range of Trigonometric Functions

All trigonometric functions are basically the trigonometric proportions of any given angle. For example, if we take the functions , , etc, we are considering these trigonometric proportions as functions. The domain and range of these trigonometric functions will...
Domain and Range of Exponential Functions

Domain and Range of Exponential Functions

The domain of exponential functions is equal to all real numbers since we have no restrictions with the values that x can take. The range of exponential functions is equal to the values above or below the horizontal asymptote. Here, we will see in detail how to find...
Domain and Range of Linear Functions

Domain and Range of Linear Functions

The domain of linear functions is equal to the entire set of real numbers of x. This is because we do not have any restrictions on the values of x. Similarly, the range of linear functions is also the entire set of real numbers in y. Here, we will look at more details...