Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

x^(4)-13x^(2)+40

$5$ ) $x^{4}-13 x^{2}+40$

View step-by-step help

View step-by-step help

Solve complex trigonomentric equations

Full solution

Q.

5

)

x^{4}-13 x^{2}+40

Factor Quadratic Equation: Let's factor the equation like a quadratic, where $x^2$ is our variable. $\newline$ $x^4 - 13x^2 + 40 = 0$ $\newline$ Think of it as $(x^2)^2 - 13(x^2) + 40 = 0$ $\newline$ Now, factor it. $\newline$ $(x^2 - 5)(x^2 - 8) = 0$
Set Equal and Solve: Set each factor equal to zero and solve for $x^2$ . $\newline$ $x^2 - 5 = 0$ and $x^2 - 8 = 0$ $\newline$ So, $x^2 = 5$ and $x^2 = 8$
Take Square Root: Now, take the square root of both sides for each equation. $\newline$ For $x^2 = 5$ , we get $x = \pm\sqrt{5}$ . $\newline$ For $x^2 = 8$ , we get $x = \pm\sqrt{8}$ , but $\sqrt{8}$ can be simplified to $2\sqrt{2}$ . $\newline$ So, $x = \pm2\sqrt{2}$ .

More problems from Solve complex trigonomentric equations

Question

Find all solutions with

0^\circ \leq \theta \leq 180^\circ

. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.

\newline

\cos(\theta) = -1

\newline

\underline{\hspace{2em}}^\circ

Posted 1 month ago

Question

Kimi's school is

15

kilometers west of her house and

8

kilometers south of her friend Franklin's house. Every day, Kimi bicycles from her house to her school. After school, she bicycles from her school to Franklin's house. Before dinner, she bicycles home on a bike path that goes straight from Franklin's house to her own house. How far does Kimi bicycle each day?

\newline

\_\_\_\_\_

Posted 1 month ago

Question

Evaluate. Write your answer as an integer or as a decimal rounded to the nearest hundredth.

\newline

\cos 35^\circ =

Posted 1 month ago

Question

Find all solutions with

-90^\circ \leq \theta \leq 90^\circ

. Give the exact answer(s) in simplest form. If there are multiple answers, separate them with commas.

\newline

\csc(\theta) = -1

\newline

\_\_\_\_\,^\circ

Posted 1 month ago

Question

Evaluate. Write your answer in simplified, rationalized form. Do not round.

\newline

\cot 30^\circ =

Posted 1 month ago

Question

The terminal side of an angle

\theta

in standard position intersects the unit circle at

(\frac{84}{85}, \frac{13}{85})

\cos(\theta)

\newline

Write your answer in simplified, rationalized form.

\newline

Posted 1 month ago

Question

-90^\circ < \theta < 90^\circ

. Find the value of

\theta

\newline

\tan(\theta) = 0

\newline

Write your answer in simplified, rationalized form. Do not round.

\newline

\theta =

^\circ

\newline

Posted 2 months ago

Question

Evaluate. Write your answer in simplified, rationalized form. Do not round.

\newline

\csc 60^\circ =

Posted 1 month ago

Question

\theta

is an acute angle. Find the value of

\theta

\newline

\sec(\theta) = \sqrt{2}

\newline

\theta =

\degree

Posted 1 month ago

Question

Evaluate. Write your answer in simplified, rationalized form. Do not round.

\newline

\cos 90^\circ =

Posted 2 months ago