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Quadratics with Parameters

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Quadratic Equations

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Quadratics with Parameters

Algebra-1

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You will find the value(s) of the parameter based on the given different conditions.

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Now You Know

After completing this tutorial, you will be able to complete the following:

  • Find the value of a parameter for which the given equation is quadratic.
  • Find the value of a parameter when the number of roots of the quadratic equation is given.
  • Find the value of a parameter when one of the quadratic equation’s roots is given.
  • Find the value of a parameter when the sum or the product of the quadratic equation’s roots is given.

Everything You'll Have Covered

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 discriminant

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.

They are:

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.

Tutorial Details

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.
Course Algebra-1
Type of Tutorial Skills Application
Key Vocabulary conditions, quadratic equation, value of the parameter