Algebra Know-It-ALL

Let’s use the commutative law for addition to rearrange the terms according to powers of

x with each power of x on its own line:

10 x^2

+j 8 x+ 10 x+ (−j 10 x)+ 15 x

+ 8 + (−j10)+j 12 + 15

= 0

We can rewrite this as

10 x^2

+ [j 8 + 10 + 15 + (−j10)]x

+ 8 + 15 + (−j10)+j 12

= 0

This simplifies to

10 x^2 + (25 −j2)x+ (23 +j2)= 0

Chapter 24

1. This function is stated in binomial factor form. To figure out whether its graph opens
   upward or downward, we must morph it into polynomial standard form by multiplying
   out the factors:

y= (x− 3)(4x− 1)

= 4 x^2 + (−x)+ (− 12 x)+ 3

= 4 x^2 − 13 x+ 3

The coefficient of x^2 is positive. That means the parabola opens upward.

2. The real zeros of the quadratic function stated in Prob. 1 can be found from the factors
   in the original version. We must solve these two first-degree equations:

x− 3 = 0

and

4 x− 1 = 0

In the top equation, we can add 3 to each side, getting x= 3. In the bottom equation, we

can add 1 to each side and then divide through by 4, obtaining x= 1/4. The real zeros of

the quadratic function are therefore x= 3 or x= 1/4.

Chapter 24 681