Mentally decide whether the solutions to each equation are real numbers or not.
18.2
Activity
Kiran was using the quadratic formula to solve the equation . He wrote this:
Then he noticed that the number inside the square root is negative and said, “This equation doesn’t have any solutions.”
Do you agree with Kiran? Explain your reasoning.
Write as an imaginary number.
Solve the equation and plot the solutions in the complex plane.
18.3
Activity
For each row, you and your partner will each solve a quadratic equation. You should each get the same answer. If you disagree, work to reach an agreement.
partner A
partner B
Student Lesson Summary
Sometimes when we use the quadratic formula to solve a quadratic equation, we get a negative number inside the square root symbol. This means that the solutions to the equation must involve imaginary numbers. For example, consider the following equation: