October 15, 2008

This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Determine the number of solutions of a quadratic equation.

It explains how to determine number of solutions of a quadratic equation. For a given general quadratic equation y = ax^{2} + bx + c, the number and type of roots can be determined by graphing it on the cartesian plane. If we do that, the x-intercepts will be the solutions or roots of the equation. If the graph intersects the x-axis only at one point, then the roots are real and equal, and the quadratic equation has only one solution. If the graph intersects the x-axis at two points, then the roots are real and distinct, and the quadratic equation has two solutions. If the does not intersect y-axis at all, then the roots are imaginary.

It explains how to determine number of solutions of a quadratic equation. For a given general quadratic equation y = ax

This FREE mini-lesson is a part of Winpossible's online course that covers all topics within Algebra I. Click on the video below to go through it. If you like it, you can buy our online course in Algebra I by clicking here.

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Solve quadratic equations with real coefficients that have complex solutions.

Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.