Chapter 7.5, Problem 1E

To determine

To describe:The signs of the terms in the given polynomial tell about its factors is to be described.

Answer to Problem 1E

Factorsare $(x+p),(x+q)$

One term out of $p$ and $q$ is negative and sum of $p$ and $q$ is $11$ .

Explanation of Solution

Given information:Given polynomial is $x^2+11x-26$ .

Calculation:

  $x^2+11x-26$

  $\begin{array}{l}p+q=\frac{b}{a}=11\\ pq=\frac{c}{a}=-26\end{array}$

  $\Rightarrow$ In the factors, $(x+p),(x+q)$ , as $(pq)$ is negative,

  $\therefore$ One term out of $p$ and $q$ is negative.

And sum of $p$ and $q$ is $11$ .