Quadratic Equations with Irrational Solutions - Group Activity

This is a challenging activity to promote students thought, creativity and discovery. The product can be used for groups of 4 members or as an individual practice (4 different versions included).

Students will practice solving quadratic equations with rational and irrational coefficients having only irrational solutions. Some of the equations are in standard form and the other have one term on the right side of the equation. Each quadratic equation must be solved by a specified method - completing the square or the quadratic formula. There are problems included, where students need to

• rationalize denominators containing radicals
• find the square of a sum or a difference between rational and irrational numbers
• find the common root between two equations

Hints are included to help students check if their ”pretty” answers are correct.

If this resource is used for group work, there is a group response sheet specially provided. There partners are instructed to calculate the sum or/and product of all their answers to corresponding problems. They record their findings, surprised to discover that their collective answers are “pretty” numbers too.

A recording worksheet is included for students to show work. All answer keys are included.