Answered: In Problem approximate the real…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter1: Equations And Graphs

Section1.CT: Chapter Test

Problem 11CT

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In Problem approximate the real solutions to each quadratic equation to two decimal places.

Expert Solution

Step 1

Given quadratic equation is $23.1 - 14.1 x - 0.002 x^{2} = 0$ .

Given quadratic equation can be written as:

$\begin{array}{rcl} 23.1 - 14.1 x - 0.002 x^{2} & = & 0 \\ - 0.002 x^{2} - 14.1 x + 23.1 & = & 0 \\ 0.002 x^{2} + 14.1 x - 23.1 & = & 0 \end{array}$

Quadratic formula for quadratic equation,

$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$

Solving using quadratic formula,

$\begin{array}{rcl} x & = & \frac{- (14.1) \pm \sqrt{{(14.1)}^{2} - 4 (0.002) (- 23.1)}}{2 (0.002)} \\ = & \frac{- 14.1 \pm \sqrt{198.81 + 0.1848}}{0.004} \\ = & \frac{- 14.1 \pm \sqrt{198.99}}{0.004} \\ = & \frac{- 14.1 \pm 14.10}{0.004} \\ = & \frac{- 14.1 + 14.1}{0.004} o r \frac{- 14.1 - 14.1}{0.004} \\ = & 0 o r 7050 \end{array}$

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