# Discriminant

- Author:
- rokas tamosiunas

## Discriminant of quadratic polynomial

Time for investigation, almost 75 min
Earlier in the course: Enough playing around with the graphs of quadratic functions & formula for zeros

**.**Goal: Students find out which part of formula above influences the number of solutions of second order polynomial.**This idea is simple, takes time for students to do and gives them opportunity to rehearse how to solve zeroes, how to express themselves mathematically.****Students are asked to do following ( in small groups)**- With Geogebra, find out second order polynomial, which has a) 2 b) 1 c) 0 zeros.
- By hand, calculate the zeros and find out, which part of the formula influences the number of solutions.
- Make your own theory. ( Formulate your theory so that it uses same letters as in the formula for zeros of second order polynomial. Write down your theory, send or show to teacher.
- Use your theory, to find out for which k, equation
**has 2 solutions, 1 solution or 0 solutions. You can use Geogebra to solve this. ( there are at least 2 possibilities to go, students use slider or CAS)**