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: 44

Answer

No real zeros. No real $x$-intercepts.

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 $H(x)=0$: $$4x^2+x+1=0$$ Comparing $4x^2+x+1$ to $ax^2+bx+c=0$ to find $a,b \text{ and } c$ $$\therefore a = 4, b=1 , c =1$$ Evaluating the discriminant $b^2-4ac$ $$b^2-4ac = (1)^2-4 \times 4 \times 1 = -15$$ Since the discriminant is negative, then the function has no real zeros.
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