James Sousa: Ex 4: Find the Zeros of a Polynomial Function with Imaginary Zeros
In #12 from the previous problem set, there are two imaginary solutions. Imaginary solutions always come in pairs. To find the imaginary solutions to a function, use the Quadratic Formula. If you need a little review on imaginary numbers and how to solve a quadratic equation with complex solutions see the Quadratic Equations chapter.
Solution: First, this quartic function can be factored just like a quadratic equation. See the Factoring Polynomials in Quadratic Form concept from this chapter for review.
Including the imaginary solutions, there are four, which is what we would expect because the degree of this function is four.
Now, set each factor equal to zero and solve.
Intro Problem Revisit First we need to change the equation to standard form. Then we can factor it.
Solving for x we get
Find all the solutions to the following functions.
1. First, graph the function.
Setting each factor equal to zero, we have:
Find all solutions to the following functions. Use any method.
Find a function with the following roots.
Writing Write down the steps you use to find all the zeros of a polynomial function.
Writing Why do imaginary and irrational roots always come in pairs?
Challenge Find all the solutions to f(x)=x5+x3+8x2+8.