Chapter 9: Q.457. (page 984)

Solve the quadratic equation.
$4 x^{4} - 5 x^{2} + 1 = 0$

Short Answer

Expert verified

The solutions are $x = \pm \frac{1}{2}$ and $x = \pm 1$ .

Step by step solution

Step 1. Given information.

The given equation is $4 x^{4} - 5 x^{2} + 1 = 0$ .

Step 2. Simplify the equation by the factorization method.

$\begin{array}{rcl} 4 x^{4} - 5 x^{2} + 1 & = & 0 \\ 4 {(x^{2})}^{2} - 5 x^{2} + 1 & = & 0 \\ 4 {(x^{2})}^{2} - x^{2} - 4 x^{2} + 1 & = & 0 \\ x^{2} (4 x^{2} - 1) - 1 (4 x^{2} - 1) & = & 0 \\ (4 x^{2} - 1) (x^{2} - 1) & = & 0 \end{array}$

Step 3. Solve the equation for x.

$\begin{array}{rcl} 4 x^{2} - 1 & = & 0 \\ 4 x^{2} & = & 1 \\ x^{2} & = & \frac{1}{4} \\ x & = & \pm \sqrt{\frac{1}{4}} \\ x & = & \pm \frac{1}{2} \end{array}$ and $\begin{array}{rcl} x^{2} - 1 & = & 0 \\ x^{2} & = & 1 \\ x & = & \pm \sqrt{1} \\ x & = & \pm 1 \end{array}$

Step 4. Simplified answer.

Hence, the required solutions are $x = \pm \frac{1}{2}$ and $x = \pm 1$ .

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Solve the quadratic equation.
$4 x^{4} - 5 x^{2} + 1 = 0$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the equation by the factorization method.

Step 3. Solve the equation for x.

Step 4. Simplified answer.

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Solve the quadratic equation.4x4-5x2+1=0

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Simplify the equation by the factorization method.

Step 3. Solve the equation for x.

Step 4. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Discrete Mathematics

Statistics

Decision Maths

Theoretical and Mathematical Physics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Solve the quadratic equation.
$4 x^{4} - 5 x^{2} + 1 = 0$