Give examples of quadratic equations with (a) two real solutions, (b) one real solution, and (c) no real solution.

1
by charitulabut

Answers

2016-06-28T22:51:50+08:00
Solve x(x – 2) = 4. Round your answer to two decimal places.I not only cannot apply the Quadratic Formula at this point, I cannot factor either.I can not claim that "x = 4, x – 2 = 4", because this is not how "solving by factoring" works. I must first rearrange the equation in the form "(quadratic) = 0", whether I'm factoring or using the Quadratic Formula. The first thing I have to do here is multiply through on the left-hand side, and then I'll move the 4 over:x(x – 2) = 4
x2 – 2x = 4
x2 – 2x – 4 = 0
Since there are no factors of (1)(–4) = –4 that add up to –2, then this quadratic does not factor. (In other words, there is no possible way that the faux-factoring solution of "x = 4, x – 2 = 4" could be even slightly correct.) So factoring won't work, but I can use the Quadratic Formula; in this case, a = 1, b = –2, and c = –4:   Copyright © Elizabeth Stapel 2000-2011 All Rights ReservedThen the answer is:  x = –1.24, x = 3.24, rounded to two places.
Too long. Do you have a shorter example of that?