Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 2 - Section 2.4 - Dividing Polynomials; Remainder and Factor Theorems - Exercise Set - Page 365: 69

Answer

No, the given statement does not make sense.

Work Step by Step

Let us suppose that we have a function $f\left( x \right)={{x}^{2}}-5x+6$ with zeros at $x=2,3$. Now, finding the solutions of the equation $f\left( x \right)=0$, gives: $\begin{align} & {{x}^{2}}-5x+6=0 \\ & {{x}^{2}}-2x-3x+6=0 \\ & x\left( x-2 \right)-3\left( x-2 \right)=0 \\ & \left( x-2 \right)\left( x-3 \right)=0 \\ \end{align}$ And, the value of x is as follows: $x=2,3$ Thus it is observed that the solution of $f\left( x \right)=0$ give us the zeros of the equation which we already had. Therefore, the given statement does not make any sense.
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