SOLUTION: x4 � 3 x2 + 2 = 0. Explain how one can use the quadratic formula to solve this equation by using a change of variable. Solve this equation completely.

Question 122284: x4 � 3 x2 + 2 = 0.
Explain how one can use the quadratic formula to solve this equation by using a change of variable. Solve this equation completely.

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Let to get

Let's use the quadratic formula to solve for u:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=1, b=-3, and c=2

Negate -3 to get 3

Square -3 to get 9 (note: remember when you square -3, you must square the negative as well. This is because .)

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator
Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator
Divide

So another answer is

So our solutions are:
or

Now remember, we let

So our solutions become

or

Now take the square root of both sides for each case

or

Answer:

So our answers are

, , , or
RELATED QUESTIONS
2. The following equation has degree 4 because the highest power of the variable x is 4: (answered by josmiceli,solver91311)

a) Is y = x^2 + 7x + 12 a quadratic equation*? Why or why not? b) Can it be solved by... (answered by josgarithmetic,macston)

Developing and Analyzing the Quadratic Formula This formula, which is called the... (answered by stanbon)

1. Use what you have learned to find the solutions of the polynomial... (answered by josgarithmetic)

Please help. I do not understand how to do this. 1) Using the quadratic equation x2 (answered by elima)

I've missed a lot of school because I've been sick and I'm trying to get all of my work... (answered by jsmallt9)

Can you please help me solve this? Factorise the quadratic expressions using the... (answered by rothauserc)

How do i solve by using the quadratic formula of x2 - 4x - 5 =... (answered by Alwayscheerful)

2. x2 � 2x � 11 = 0 Use the Quadratic Formula to solve each equation. (answered by jim_thompson5910,ewatrrr)