Chapter 8.5, Problem 48PPE

a.

To determine

To explain: What information we get for the sign of p and q

Answer to Problem 48PPE

Both p and q must be of opposite signs

Explanation of Solution

Given information: $x^2+13x-30=(x+p)(x+q)$

Both p and q must be of opposite signs, because in equation $x^2+13x-30$ , on comparing with $a{x}^2+bx+c$ , we can see that c(=30) is negative here, which can be possible only when p and q are of opposite signs. if both p and q are of same sign, then it can not be possible.

b.

To determine

To explain: Which number p or q is a negative integer?

Answer to Problem 48PPE

Here q is negative

Explanation of Solution

Given information: $x^2+13x-30=(x+p)(x+q)$ and $\left|p\right|>\left|q\right|$

Here q must be a negative integer, because in equation $x^2+13x-30$ , on comparing with $a{x}^2+bx+c$ , we see that b(=13) is positive, this is possible only when p is positive, because it is given that $\left|p\right|>\left|q\right|$