Chapter 9: Q.455. (page 984)

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

Short Answer

Expert verified

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

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.

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

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.

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

Step 6. Simplified answer.

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

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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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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

Applied Mathematics

Decision Maths

Logic and Functions

Pure Maths

Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

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