You will find the value(s) of the parameter based on the given different conditions.
After completing this tutorial, you will be able to complete the following:
A Quadratic Equation
A quadratic equation is a nonlinear equation written in general form as ax2 + bx + c = 0, where a, b, c are real numbers and a ? 0.
Solution of a Quadratic Equation
A solution of a quadratic equation is a value that satisfies the quadratic equation.
The expression (b2 - 4ac) of the related quadratic equation ax2 + bx + c = 0.
When the discriminant is a negative value (D < 0), this means that the quadratic equation has no real roots; that is, the roots are imaginary, and not in the real number system.
When the discriminant is equal to zero (D = 0), the quadratic equation has one distinct real root.
When the discriminant is a positive value (D >0), the quadratic equation has two real roots.
Quadratics with parameters
Quadratic equations involving a parameter(s) are called quadratics with parameters. The value of parameters vary based on the conditions given.
Some of the conditions that will affect the value of the parameter are given in the Activity Object.
The number of roots is given
One of the roots is given
The sum of the roots is given
The product of the roots is given
There are specific methods for solving for the value of the parameter when each of these situations is encountered, and all are discussed in the Activity Object.
|Approximate Time||30 Minutes|
|Pre-requisite Concepts||Learners should be familiar with the definition of a quadratic equation, discriminant, finding the number of roots of a quadratic equation, product of the roots of a quadratic equation, roots of a quadratic equation, solving a linear equation, and the sum of the roots of a quadratic equation.|
|Type of Tutorial||Skills Application|
|Key Vocabulary||conditions, quadratic equation, value of the parameter|