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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q. 527 (page 987)

In the following exercises, solve each inequality algebraically and write any solution in interval notation:
$- x^{2} + x - 6 > 鈥� 0$

Short Answer

Expert verified

The inequality $- x^{2} + x - 6 > 鈥� 0$ has no solution.

Step by step solution

01

Step 1. Given information.

We have:

$- x^{2} + x - 6 > 鈥� 0$

02

Step 2. Solve the inequality.

Change the sign $>$ with $=$ and solve by quadratic formula.

$- x^{2} + x - 6 = 0 For 鈥� a 鈥� quadratic 鈥� equation 鈥� of 鈥� the 鈥� form 鈥� a x^{2} + b x + c = 0 鈥� the 鈥� solutions 鈥� are 鈥� x_{1, 鈥� 2} = \frac{- b 卤 \sqrt{b^{2} - 4 a c}}{2 a} For 鈥� a = - 1, 鈥� b = 1, 鈥� c = - 6 x_{1, 鈥� 2} = \frac{- 1 卤 \sqrt{1^{2} - 4 (- 1) (- 6)}}{2 (- 1)} x_{1, 鈥� 2} = \frac{- 1 卤 \sqrt{23} i}{2 (- 1)} x = \frac{1}{2} - i \frac{\sqrt{23}}{2}, 鈥� x = \frac{1}{2} + i \frac{\sqrt{23}}{2}$

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