Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 2 - Linear and Quadratic Functions - Section 2.3 Quadratic Functions and Their Zeros - 2.3 Assess Your Understanding - Page 146: 74

Answer

Zero:$1$ $x$-intercept: $1$

Work Step by Step

To find the zeros of a function $f$, solve the equation $f(x)=0$ The zeros of the function are also the $x-$intercepts. Let $f(x)=0$: $$x+\sqrt{x}-2=0$$ Let $u=\sqrt{x}$, the original equation becomes $$u^2+u-2=0$$ By factoring $$(u+2)(u-1) = 0$$ Use the Zero-Product Property by equating each factor to zero, then solve each equatin to obtain: \begin{align*} u +2&=0 &\text{ or }& &u-1=0\\ u &= -2 &\text{ or }& &u=1\\ \end{align*} To solve for $x$, we use $u=\sqrt{x}$ For $u=-2$ $$\sqrt{x}=-2 \hspace{5pt} \to \hspace{5pt} \text{No Solution}$$ For $u=1$ $$\sqrt{x}=1$$ $$\therefore x = 1$$ $\therefore x =1$
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