Algebra Know-It-ALL

538 Review Questions and Answers

Question 28-10

Consider the system of equations we evaluated in Answer 27-10, where we found that there

are no real solutions:

y=x^3 + 3 x^2 + 3 x+ 1

and

y=x^3 + 6 x^2 + 12 x+ 8

How can we sketch an approximate graph of this system, showing that there are no real solutions?

Answer 28-10

We can tabulate and plot enough points in both functions to get clear images of their curves, and to

show that they do not intersect (although they come close). Table 30-5 compares some values of x,

some values of the first function, and some values of the second function. Figure 30-11 shows the

curves. On the x axis, each increment is 1 unit. On the y axis, each increment is 10 units.

Chapter 29

Question 29-1

If we say that the common logarithm of a certain number p is equal to q, what do we mean?

Answer 29-1

The common logarithm (or common log) of a number is the power to which we must raise 10

to get that number. If we say that the common log of p is equal to q, we mean

p= 10 q

x

y

(–1,0)

Figure 30-10 Illustration for Answer 28-9. The first function

is graphed as a solid curve; the second function

is graphed as a dashed curve. The real-number

solution appears as a point where the curves

intersect. On the x axis, each increment is 1/2 unit.

On the y axis, each increment is 5 units.