Practice Makes Perfect Algebra I Review and Workbook by Carolyn Wheater

Author:Carolyn Wheater
Language: eng
Format: epub
Publisher: McGraw-Hill Education
Published: 2018-01-06T05:00:00+00:00

The two solutions that are typical of quadratic equations come from that ± sign.

The discriminant

One portion of the quadratic formula, called the discriminant, can give you useful information about the number and type of solutions your equation has. The radicand, b2 − 4ac, tells you whether you have one real solution, two real solutions, or no real solutions, and sometimes that’s all you need to know.

If b2 − 4ac is positive, the equation has two real solutions. You have a positive number under the radical, so you get the positive and the negative square root and produce two solutions.If b2 − 4ac equals 0, the positive and negative square roots are both 0, so you end up with only one solution, This is sometimes called a double root, since it really is two solutions that are exactly the same. If b2 − 4ac is negative, you know it’s impossible to find the square root of a negative number in the real numbers. (Later in your math career, you’ll learn about a set of numbers larger than the reals, where negative numbers do have square roots.) So if the discriminant is negative, there are no real solutions.

You can get one more bit of information from the discriminant. If the discriminant is positive and it’s a perfect square, the two solutions will be rational numbers, but if the discriminant is positive and not a perfect square, the two solutions will be irrational.

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