6.5 solving by square roots
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This document discusses using square roots to solve quadratic equations. It explains that square roots are the opposite of squaring a number, and that quadratic equations of the form x^2 = a can be solved using plus or minus the square root of a. The document provides examples of solving equations by taking the square root of both sides and leaving answers in radical form. It also discusses that some equations may have imaginary number solutions when the number under the radical is negative.
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6.5 solving by square roots
- 1. 6.5 Solving using Square Roots
- 2. What is a Square Root? The opposite of squaring a number. If r2 = s, then Ex: is called a radical sign The expression is a radical
- 3. Solving Equations Square roots can be used to solve some quadratic equations. For example: has two solutions, Usually written is read “plus or minus”
- 4. To Solve: Get the squared part by itself. Take the square root of both sides. Leave answers in radical form, no decimals! Don’t forget the !
- 8. Non-Real Solutions? Not all quadratic equations have real number solutions. Example: x2 = -1 has no real solution. (A number squared can’t be negative.)
- 9. Imaginary Numbers Imaginary numbers are numbers that cannot physically exist in real life. The imaginary unit:
- 10. Since , i can be used to write the square root of any negative number. If r is a positive real #, then Examples:
- 11. Imaginary Solutions Solve for x. x2 = -16
- 12. Example: Solve: x2 + 3 = -24
- 13. Example: Solve: 3x2 + 10 = -26
- 14. You Try! Solve 2x2 + 26 = -10