Math Resource. Algebra by HOLT MCDOUGAL

By HOLT MCDOUGAL

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Any terminating or repeating decimal can be represented as a ratio of two numbers (a fraction) and is a rational number. All of the remaining decimals on the number line that neither terminate nor repeat are known as irrational numbers. The majority of irrational numbers arise as the roots of numbers. , but the decimal neither terminates nor repeats. 4495, but it too neither terminates nor repeats. Many cubic roots, designated x or x 1 3 , are irrational, as are most 4th and higher degree roots of numbers.

For example, the concept of zero, a number representing nothing, was quite simply overlooked until the Babylonians stumbled upon it. ” Imaginary numbers arise when the square roots of negatives are computed. If we were asked to solve the equation x 2 = 10 , there would be two solutions: x = 10 and x = − 10 . Frequently, though, mathematics arrives at equations such as x 2 = −4 , and, until recently, mathematicians were forced to write impotently, “no solution,” victims of a number system we devised for ourselves.

The equation is already written in the proper form for the quadratic formula. Here, a = 6, b = -1, and c = -12. x= x= − b ± b 2 − 4ac 2a + 1 ± 1 − 4(6)( −12) 2(6) 1 ± 289 12 1 + 17 1 − 17 x= or x = 12 12 18 3 −16 4 x= = or x = =− 12 2 12 3 x= Example: Solve x2 – 10x + 23 = 0 using the quadratic formula. Solution: This equation is already put in the proper form to apply the quadratic formula. As it is written, we have a = 1, b = -10, and c = 23. x= x= − b ± b 2 − 4ac 2a + 10 ± 100 − 4(1)(23) 2(1) x= 10 ± 8 2 x= 10 ± 2 2 2 10 + 2 2 10 − 2 2 or x = 2 2 x=5+ 2 or x = 5 − 2 x= 36 ALGEBRA RESOURCE DEMIDEC RESOURCES © 2001 Example: Solve the quadratic equation x2 = -10x – 50 using the quadratic formula.

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