October 15, 2008

This resource has been contributed by Winpossible, and can also be accessed on their website by clicking here - Solution and discriminant in the quadratic formula.

In this mini-lesson, you'll learn how to calculate and interpret the discriminant in the quadratic formula. In a quadratic equation ax^{2} + bx + c = 0, the roots are given by x = {–b ± ?(b^{2} – 4ac)}/ 2a and the discriminant is b^{2} - 4ac. The quadratic equation ax^{2} + bx + c = 0 has two solutions or roots, and these roots depend on the value of b^{2} – 4ac which is denoted by ?. If ? = 0, the discriminant is zero, that means there is only one real number solution. If ? › 0, the discriminant is a positive number, that means there are two distinct real number solutions. If ? ‹ 0 i.e. negative, there are two distinct roots, each of which is a complex number. A complex number is of the form a + ib; where and b are real numbers and i is the imaginary number with the property i^{2} = –1. E.g. (2 + ?–36) is a complex number.

.In this mini-lesson, you'll learn how to calculate and interpret the discriminant in the quadratic formula. In a quadratic equation 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 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.