Solutions to quadratic equations

The  exercise appears under the Algebra II Math Mission. This exercise concentrates on the discriminant as a tool to determine the nature of the roots of a quadratic equation.

Types of Problems
There is one type of problem in this exercise:


 * 1) Determine the nature of the solutions: This problem provides a quadratic equation. The student is asked to figure out the nature of the solutions to the quadratic and select the correct description from a multiple choice list.Stqe1.png

Strategies
Knowledge of the quadratic formula and strength in arithmetic are encouraged to ensure success on this exercise.
 * 1) When the discriminant, $$ D=b^2-4ac$$ is negative the quadratic formula will yield imaginary solutions.
 * 2) If D<0, there are two complex solutions since the square root of a negative number is complex.
 * 3) If D=0, there is one rational solution since the square root of zero is only zero.
 * 4) If D>0, then there are two solutions. They are rational if radicals are avoided, so it D is a perfect square. Otherwise they will be irrational.
 * 5) One cannot have a single complex solution if the coefficients are real numbers.

Real-life Applications

 * 1) Quadratics are used to model acceleration due to gravity and are useful in the inverse square law from physics.