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Quadratic Formula: Example 2
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Let's apply these concepts:
Quadratic Formula
Factoring
Completing the Square
Discriminant
as we solve
x
2
–
x
– 12 = 0
List the values of A, B, and C for use in the quadratic formula.
A = 1, B = – 1, C = – 12
Substitute these values in the
Quadratic Formula
.
Simplify the radical.
Use this result to solve for
x
.
Find the solution which corresponds to choosing +7.
Find the solution which corresponds to choosing – 7.
Check
x
= 4 in the
original equation
.
For
x
= 4 in
x
2
–
x
– 12 = 0, we get
4
2
– 4– 12 = 16 – 16 = 0 OK
Check
x
= – 3 in the
original equation.
For
x
= – 3 in
x
2
–
x
– 12 = 0, we get
(– 3)
2
– (– 3)– 12 = 9 + 3 – 12 = 0 OK
Factoring:
As a review, try factoring
x
2
–
x
– 12 = 0
We get (
x
– 4)*(
x
+ 3) = 0
Apply the zero product rule.
We get
x – 4 = 0 and
x
+ 3 = 0, or
x = 4 and
x
= – 3, just as with the quadratic formula.
As further review, let's try
Completing-the-Square
on this same problem:
x
2
–
x
– 12 = 0.
What do we do first?
Move the constant term to the other side.
Do it.
x
2
–
x
= 12
What do we need to add to each side in order to make the left side a perfect square?
Do it.
Do the "squares".
Combine the constants on the right-hand side and write the left side as a perfect square.
Take the square root of both sides.
Solve for
x
.
, as before.
Discriminant:
Let's review this concept. Write the general expression for the discriminant in terms of A, B, C.
B
2
– 4AC
Substitute the values from this example:
A = 1, B = – 1, C = – 12
(– 1)
2
– 4(1)*(– 12)
Do the math.
1 – (– 48) = 1 + 48 = 49
Is this consistent with the two roots,
x = 4, and
x
= – 3, which we found?
Yes.
Why?
When the discriminant is positive, there are two distinct real roots.
The end. If you found this helpful and would recommend that I create more pages like this one, please let me know:
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General Contents
Detailed Contents
Index