Chapter 9: Q. 161 (page 906)

In the following exercises, solve. $2 x^{4} - 7 x^{2} + 3 = 0$

Short Answer

Expert verified

Solution for equation will be

$x = + \sqrt{3}$
$x = - \sqrt{3}$
$x = + \sqrt{\frac{1}{2}}$
$x = - \sqrt{\frac{1}{2}}$

Step by step solution

Step 1. Given Data

Quadratic Equation is $2 x^{4} - 7 x^{2} + 3 = 0$

Step 2. To Find

We have to solve it and find the value of x.

Step 3. Explanation

Let the value of $x^{2} = u$

Then the equation is -

$2 x^{4} - 7 x^{2} + 3 = 0$

$2 {(x^{2})}^{2} - 7 x^{2} + 3 = 0$

Put the value of $x^{2} = u$

$2 u^{2} - 7 u + 3 = 0$

$(u - 3) (u - \frac{1}{2}) = 0$

By using Zero product property -

$u - 3 = 0$ , $u - \frac{1}{2} = 0$

$u = 3$ , $u = \frac{1}{2}$

Step 4. Calculation

Replace u with $x^{2}$

$x^{2} = 3$ , $x^{2} = \frac{1}{2}$

Using the square root property -

$x = \pm \sqrt{3}$ , $x = \pm \sqrt{\frac{1}{2}}$

There are four solutions -

$x = + \sqrt{3}$
$x = - \sqrt{3}$
$x = + \sqrt{\frac{1}{2}}$
$x = - \sqrt{\frac{1}{2}}$

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In the following exercises, solve. $2 x^{4} - 7 x^{2} + 3 = 0$

Short Answer

Step by step solution

Step 1. Given Data

Step 2. To Find

Step 3. Explanation

Step 4. Calculation

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In the following exercises, solve. 2x4-7x2+3=0

Short Answer

Step by step solution

Step 1. Given Data

Step 2. To Find

Step 3. Explanation

Step 4. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Mechanics Maths

Calculus

Applied Mathematics

Theoretical and Mathematical Physics

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, solve. $2 x^{4} - 7 x^{2} + 3 = 0$