Answered: In Problem approximate the real…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

ChapterR: Algebra Reference

SectionR.4: Equations

Problem 16E

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Question

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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