Equations Quadratic in Form ;_;

In summary, the conversation is about solving the equation y^4 + 3y^2 - 4 = 0 by using the quadratic formula. The person realizes their mistake in forgetting to include a plus/minus symbol when taking the square root, resulting in two solutions: 2i and -2i.
  • #1
Matthewkind
56
0

Homework Statement


y^4 + 3y^2 - 4 = 0


Homework Equations





The Attempt at a Solution


The base, I know, is y^2. So in order to make this a quadratic equation, we come up with an arbitrary variable, say α, which is equal to the base. Re-writing this, we get:

(y^2)^2 + 3(y^2) - 4 = 0
α = y^2
α^2 + 3α - 4 = 0

So now it's a quadratic equation.
Factoring, we get:

(α - 1) (α + 4) = 0

Setting both of these equal to zero, we get:

α = 1 and α = -4

This next part is where I'm lost, so maybe one of you bright people can show me where I'm making my mistake.

We start with α = -4.

Since α = y^2, -4 must = y^2 too.

-4 = y^2

Solving this for y, we get:

y = sqrt(-4) = 2i.

However, in the text - without any explanation as to how this occurs (which is what is confusing me about these problems) - it says that the two solutions are 2i and -2i.

Can someone please explain this step to me. D:
 
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  • #2
Oh. Wait. I think I figured it out. When you take the square root of something we have to remember to put plus/minus, right? ;_; Maybe it's time to go back to radical rules! How embarrassing! Sorry, Physics Forums!
 
  • #3
Matthewkind said:
Oh. Wait. I think I figured it out. When you take the square root of something we have to remember to put plus/minus, right? ;_; Maybe it's time to go back to radical rules! How embarrassing! Sorry, Physics Forums!

Yep that's exactly what it is you can have to answers ±√.
 

FAQ: Equations Quadratic in Form ;_;

What is an equation quadratic in form?

An equation quadratic in form is an equation that can be written in the form ax^2 + bx + c = 0, where a, b, and c are real numbers and a is not equal to 0.

What is the standard form of an equation quadratic in form?

The standard form of an equation quadratic in form is ax^2 + bx + c = 0, where a, b, and c are real numbers and a is not equal to 0.

How do you solve an equation quadratic in form?

An equation quadratic in form can be solved using various methods such as factoring, completing the square, or using the quadratic formula.

What is the quadratic formula?

The quadratic formula is a formula used to solve equations quadratic in form. It is written as x = (-b ± √(b^2 - 4ac)) / 2a, where a, b, and c are the coefficients of the equation in standard form.

What are some real-life applications of equations quadratic in form?

Equations quadratic in form can be used to model various real-life situations such as projectile motion, optimization problems, and financial calculations. They can also be used in fields such as engineering, physics, and economics.

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