Solving Quadratic Inequalities (2.12.1)

Question 1

• Solving inequalities:
• Factor where possible.
• Determine the points where each factor equals zero.
• Determine what intervals produce results that satisfy the inequality as originally stated

Answer 1

• Solving inequalities:
• Factor where possible.
• Determine the points where each factor equals zero.
• Determine what intervals produce results that satisfy the inequality as originally stated

Question 2

• Remember that multiplying or dividing by a negative number reverses the inequality.

Answer 2

• Remember that multiplying or dividing by a negative number reverses the inequality.

Question 3

• Remember that graphing on a number line is the best way to spot all the possibilities.

Answer 3

• Remember that graphing on a number line is the best way to spot all the possibilities.

Question 4

In this example, you are able to factor easily.
By factoring you can solve for the points where the
polynomial equals zero
Now, use a number line to determine the points in the
solution. For this example, your main concern is that the
product be greater than 0.
To get a product greater than 0, multiply numbers with the
same signs; i.e., either both positive or both negative.
To determine your solution, pick a number from each interval
and substitute it in for x. In this example, your intervals are:
(1) all the numbers +3/2.
Do the arithmetic and see if your result matches the inequality.
For example, try –5 from the left interval, 0 from the middle
interval, and +3 from the right interval.
–5: (–10–3)(–5+4) = 13, > 0; it works.
0: (0–3)(0+4) = –12, 0; it works.
This shows that your solution set is all the numbers less than
–4 and greater than 3/2.

Answer 4

In this example, you are able to factor easily.
By factoring you can solve for the points where the
polynomial equals zero
Now, use a number line to determine the points in the
solution. For this example, your main concern is that the
product be greater than 0.
To get a product greater than 0, multiply numbers with the
same signs; i.e., either both positive or both negative.
To determine your solution, pick a number from each interval
and substitute it in for x. In this example, your intervals are:
(1) all the numbers +3/2.
Do the arithmetic and see if your result matches the inequality.
For example, try –5 from the left interval, 0 from the middle
interval, and +3 from the right interval.
–5: (–10–3)(–5+4) = 13, > 0; it works.
0: (0–3)(0+4) = –12, 0; it works.
This shows that your solution set is all the numbers less than
–4 and greater than 3/2.