PRECALCULUS:GRAPHICAL,...-NASTA ED.
PRECALCULUS:GRAPHICAL,...-NASTA ED.
10th Edition
ISBN: 9780134672090
Author: Demana
Publisher: PEARSON
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Chapter P.5, Problem 69E
Solution

a.

The value of c for which the given equation has four solutions.

  c=1

Given:

The equation x2−4=c .

Concept used:

  • The absolute value function, if x=a , then the solutions are x=±a .

Calculation:

In order to have 4 solutions, the value of c must be something for which 4±c must be greater than 0. So the value of c must be greater than 0 and less than 4.

Thus, one such value of c is 1 .

b.

The value of c for which the given equation has three solutions.

  c=4

Given:

The equation x2−4=c .

Concept used:

  • The absolute value function, if x=a , then the solutions are x=±a .

Calculation:

In order to have 3 solutions, the value of c must be something for which 4−c must be equal to 0. Since the value of absolute value function cannot be negative, the value of c must be 4.

Thus, one such value of c is 4.

c.

The value of c for which the given equation has two solutions.

  c=6

Given:

The equation x2−4=c .

Concept used:

  • The absolute value function, if x=a , then the solutions are x=±a .

Calculation:

In order to have 2 solutions, the value of c must be something for which 4±c must be positive and negative once. So, the value of c must be greater than 4.

Thus, one such value of c is 6.

d.

The value of c for which the given equation has no solutions.

  c=−2

Given:

The equation x2−4=c .

Concept used:

  • The absolute value function, if x=a , then the solutions are x=±a .

Calculation:

In order to have no solutions, the value of c must be something negative number because the value of absolute value function cannot be negative.

Thus, one such value of c is c=−2 .

e.

Is there any other number of solutions possible for the given function?

  NO

Given:

The equation x2−4=c .

Concept used:

  • The absolute value function, if x=a , then the solutions are x=±a .

Calculation:

Since the term inside the absolute value sign is quadratic, so there can be at most 4 solutions for the given function.

Thus, there is no other possible number of solutions for the given equation.

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Chapter P.5, Problem 68E
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Chapter P.5, Problem 70E

Chapter P Solutions

PRECALCULUS:GRAPHICAL,...-NASTA ED.

Ch. P.1 - Prob. 1QRCh. P.1 - Prob. 2QRCh. P.1 - Prob. 3QRCh. P.1 - Prob. 4QRCh. P.1 - Prob. 5QRCh. P.1 - Prob. 6QRCh. P.1 - Prob. 7QRCh. P.1 - Prob. 8QRCh. P.1 - Prob. 9QRCh. P.1 - Prob. 10QR
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