Chapter 12: Q43. (page 637)

Solve each equation.
$x^{4} - 5 x^{2} + 4 = 0$

Short Answer

Expert verified

The solutions are-2, -1, 1and2.

Step by step solution

Step 1. Given Information.

Given, to solve the equation $x^{4} - 5 x^{2} + 4 = 0$ .

Step 2. Calculation.

Solving the equation:

$\begin{array}{l} {(x^{2})}^{2} - 5 (x^{2}) + 4 = 0 \\ {(x^{2})}^{2} - (x^{2}) - 4 (x^{2}) + 4 = 0 (Writingitinthequadraticform) \\ (x^{2}) (x^{2} - 1) - 4 (x^{2} - 1) = 0 \\ (x^{2} - 1) (x^{2} - 4) = 0 (Factoringthetrinomial) \\ (x^{2} - 1^{2}) (x^{2} - 2^{2}) = 0 \\ (x - 1) (x + 1) (x - 2) (x + 2) = 0 (Factoringeachdifferenceofsquares) \end{array}$

Using the Zero Product Property:

$\begin{array}{l} x - 1 = 0 or x + 1 = 0 or x - 2 = 0 or x + 2 = 0 \\ x = 1 or x = - 1 or x = 2 or x = - 2 \end{array}$

Step 3. Conclusion.

Hence, the solutions are -2, -1, 1 and 2.

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Solve each equation.
$x^{4} - 5 x^{2} + 4 = 0$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

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Solve each equation.x4-5x2+4=0

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Discrete Mathematics

Calculus

Geometry

Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Solve each equation.
$x^{4} - 5 x^{2} + 4 = 0$