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ZingPath: Quadratic Equations

Roots and Coefficients of a Quadratic Equation

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Quadratic Equations

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Roots and Coefficients of a Quadratic Equation

Algebra-1

Learning Made Easy

You will apply the formulas for the sum or product of the roots of a quadratic equation to calculate various expressions and write a quadratic equation whose roots are given.

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Now You Know

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

  • Identify the relationship between the roots and coefficients of a quadratic equation.
  • Determine the sum and product of the roots of a quadratic equation without actually finding them.
  • Calculate the values of expressions using the formulas for the sum and product of the roots of a quadratic equation.
  • Write a quadratic equation whose roots are given.

Everything You'll Have Covered

Quadratic Functions vs. Quadratic Equations

A quadratic function is a nonlinear function written in the standard form When the function is set to zero, it is then called a quadratic equation. The x-value for f(x) = 0 is called a zero of the quadratic function, and the x-value for which the quadratic equation is satisfied is called the root of that equation. We can graph a quadratic function, and its graph is called a parabola. The x-intercepts are the x-coordinates of the points where the parabola intersects the x-axis. Note that these values are the roots of the related quadratic equation.

We can also graph a different parabola with the same x-intercepts.

Quadratic equations solved

A quadratic equation in the form can be solved using a variety of methods. The most common method used is to factor the equation. Then, using the zero product property, each factor can be set equal to zero. The resulting linear equation can be solved for x, providing the quadratic's root.

Tutorial Details

Approximate Time 25 Minutes
Pre-requisite Concepts Learners should be familiar with operations with fractions and perfect square trinomials.
Course Algebra-1
Type of Tutorial Skills Application
Key Vocabulary roots, quadratic equation, sum of the roots