Match each equation in standard form to its factored form and its complex solutions.
,
5, -5
,
17.2
Activity
Sometimes the Solutions Aren't Real Numbers
What are the complex solutions to these equations? Check your solutions by substituting them into the original equation.
17.3
Activity
Finding Complex Solutions
Solve these equations by completing the square to find all complex solutions.
17.4
Activity
Can You See the Solutions on a Graph?
How many real solutions does each equation have? How many non-real solutions?
How do the graphs of these functions help us answer the previous question?
Student Lesson Summary
Sometimes quadratic equations have real solutions, and sometimes they do not. Here is a quadratic equation with equal to a negative number (assume is positive):
This equation has imaginary solutions and . By similar reasoning, an equation of the form:
has non-real solutions if is positive. In this case, the solutions are and .
It isn’t always clear just by looking at a quadratic equation whether the solutions will be real or not. For example, look at this quadratic equation:
We can always complete the square to find out what the solutions will be:
This equation has non-real, complex solutions and .
Glossary
None
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