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: 50


Zero: $-\dfrac{5}{2}$ $x$-intercept: $-\dfrac{5}{2}$

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 $g(x)=0$: $$4x^2+20x+25=0$$ Comparing $4x^2+20x+25=0$ to $ax^2+bx+c=0$ to find $a,b \text{ and } c$: $$\therefore a = 4, b=20 , c =25$$ Evaluating the discriminant $b^2-4ac$ $$b^2-4ac = (20)^2-4 \times 4 \times 25 = 0$$ Since the discriminant is equal to zero, then there is a real repeated root. The quadratic formula is given by: $$x= \dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$$ $$x= \dfrac{-20\pm \sqrt{0}}{2\times 4}$$ $$x=\dfrac{-20\pm 0}{8}$$ $\therefore x =-\dfrac{5}{2}$
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