Q.455. Solve the quadratic equation.x4-... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 9: Q.455. (page 984)

Solve the quadratic equation.
$x^{4} - 14 x^{2} + 24 = 0$

Short Answer

Expert verified

The solutions are $x = 卤 \sqrt{2}$ and $x = 卤 2 \sqrt{3}$ .

Step by step solution

Step 1. Given information.

The given equation is $x^{4} - 14 x^{2} + 24 = 0$ .

Step 2. Rewrite the equation by substituting x2=u.

$\begin{array}{rcl} x^{4} - 14 x^{2} + 24 & = & 0 \\ {(x^{2})}^{2} - 14 x^{2} + 24 & = & 0 \\ u^{2} - 14 u + 24 & = & 0 鈰� 鈰� 鈰� (x^{2} = u) \end{array}$

Step 3. Simplify the above equation by factorization.

$\begin{array}{rcl} u^{2} - 14 u + 24 & = & 0 \\ u^{2} - 12 u - 2 u + 24 & = & 0 \\ u (u - 12) - 2 (u - 12) & = & 0 \\ (u - 12) (u - 2) & = & 0 \end{array}$

Step 4. Now apply the zero product property and solve for u.

$\begin{array}{rcl} u - 12 & = & 0 \\ u & = & 12 \end{array}$ and $\begin{array}{rcl} u - 2 & = & 0 \\ u & = & 2 \end{array}$

Step 5. Replace u with x2 and solve for x.

$\begin{array}{rcl} u & = & 12 \\ x^{2} & = & 12 \\ x & = & 卤 \sqrt{12} \\ x & = & 卤 2 \sqrt{3} \end{array}$ and $\begin{array}{rcl} u & = & 2 \\ x^{2} & = & 2 \\ x & = & 卤 \sqrt{2} \end{array}$

Step 6. Simplified answer.

Hence, the required solutions are $x = 卤 \sqrt{2}$ and $x = 卤 2 \sqrt{3}$ .

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91影视

Solve the quadratic equation.
$x^{4} - 14 x^{2} + 24 = 0$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Rewrite the equation by substituting x2=u.

Step 3. Simplify the above equation by factorization.

Step 4. Now apply the zero product property and solve for u.

Step 5. Replace u with x2 and solve for x.

Step 6. Simplified answer.

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91影视

Solve the quadratic equation.x4-14x2+24=0

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Rewrite the equation by substituting x2=u.

Step 3. Simplify the above equation by factorization.

Step 4. Now apply the zero product property and solve for u.

Step 5. Replace u with x2 and solve for x.

Step 6. Simplified answer.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Mechanics Maths

Calculus

Pure Maths

Geometry

Logic and Functions

Study anywhere. Anytime. Across all devices.

Solve the quadratic equation.
$x^{4} - 14 x^{2} + 24 = 0$