Intermediate Algebra (11th edition)

Using the Discriminant

Find kso that will have exactly one rational solution.

The equation will have only one rational solution if the discriminant is 0.

Here,.

Value of the discriminant

Set the discriminant equal to 0 and solve for k.

Add 144.

or Square root property

The equation will have only one rational solution if or

NOW TRY

k= 12 k=-12.

k= 12 k=- 12

k^2 = 144

k^2 - 144 = 0

=k^2 - 144

=k^2 - 4192142 a=9, b=k, and c= 4

b^2 - 4 ac

9 x^2 +kx+ 4 = 0

EXAMPLE 5

510 CHAPTER 9 Quadratic Equations, Inequalities, and Functions

NOW TRY
EXERCISE 5
Find kso that the equation
will have exactly one rational
solution.

4 x^2 +kx+ 25 = 0

NOW TRY ANSWER
5.20, - 20

Complete solution available
on the Video Resources on DVD

Concept Check Answer each question in Exercises 1– 4.

1.An early version of Microsoft Wo r dfor Windows included the 1.0 edition of Equation

Editor. The documentation used the following for the quadratic formula. Was this cor-

rect? If not, correct it.

2.The Cadillac Bar in Houston, Texas, encourages patrons to write (tasteful) messages on

the walls. One person wrote the quadratic formula, as shown here. Was this correct? If

not, correct it.

3.A student incorrectly solved as follows. WHAT WENT WRONG?

Solution set:

4.A student claimed that the equation cannot be solved using the quadratic

formula because there is no first-degree x-term. Was the student correct? If not, give the

values of a, b, and c.

2 x^2 - 5 = 0

e

1

2

 25 f

x=

1

2

 25

x=

5  25

10

x=

- 1 - 52  21 - 522 - 4152112

2152

5 x^2 - 5 x+ 1 = 0

x=

• b 2 b^2 - 4 ac
  2 a

x=-b

2 b^2 - 4 ac

2 a

9.2 EXERCISES