# Finding Solutions for y^4+4y-69 - Without Advanced Math Tools

• phillyolly
In summary, the conversation discusses solving the expression y^4+4y-69 and finding solutions without using sophisticated math tools. The speaker suggests manually plugging in values and asks for other efficient methods. It is mentioned that quartic equations are difficult to solve analytically and there are ways to find approximate solutions.
phillyolly

## Homework Statement

Solving y^4+4y-69, I got the following:
By manually plugging in, I found that y= -3 and y=2.76.

However, I would like to ask you if there are other good, efficient ways to find solutions?
(Without using sophisticated math tools. Imagine, I have this prob on the exam)

Thank you!

phillyolly said:

## Homework Statement

Solving y^4+4y-69
You can't "solve" an expression. You can, however, solve an equation or inequality. Is the equation y^4 + 4y - 69 = 0?
phillyolly said:
, I got the following:
By manually plugging in, I found that y= -3 and y=2.76.

However, I would like to ask you if there are other good, efficient ways to find solutions?
(Without using sophisticated math tools. Imagine, I have this prob on the exam)

Thank you!
I don't know of any ways to solve quartic (fourth-degree) equations analytically, but there might be some. There are ways to solve cubics (third-degree), but even they are fairly involved to solve.

If you don't require exact solutions, there are lots of ways to find approximate solutions, such as Newton's method, and quite a few others.

## 1. How can I solve the equation y^4+4y-69 without using advanced math tools?

One approach is to use factoring. First, try to find any common factors between the terms. In this case, there are no common factors. Then, try to factor the expression by grouping. For example, we can group the first two terms together and the last two terms together: (y^4+4y) - (69). This can be rewritten as y(y^3+4) - 69. Since there is no common factor between y and (y^3+4), we can't factor further. Therefore, the expression cannot be simplified without using advanced math tools.

## 2. Can I use the quadratic formula to solve y^4+4y-69?

No, the quadratic formula can only be used to solve equations in the form of ax^2+bx+c=0, where a, b, and c are constants. Our equation, y^4+4y-69, is not in this form and therefore cannot be solved using the quadratic formula.

## 3. Is it possible to solve y^4+4y-69 by substitution?

No, substitution is usually used to solve systems of equations, where there are two or more equations with multiple variables. In our equation, there is only one variable (y) and no other equations to substitute it into. Therefore, substitution cannot be used to solve this equation.

## 4. Can I use logarithms to solve y^4+4y-69?

No, logarithms are used to solve exponential equations, where the variable is in the exponent. In our equation, the variable is not in the exponent and therefore logarithms cannot be used to solve it.

## 5. Are there any other methods to solve y^4+4y-69 without advanced math tools?

Yes, another approach is to use the rational root theorem. This theorem states that if a polynomial has rational roots, they must be in the form of p/q, where p is a factor of the constant term and q is a factor of the leading coefficient. In our equation, the constant term is -69 and the leading coefficient is 1. Therefore, the only possible rational roots are ±1, ±3, ±23, and ±69. By substituting these values into the equation, we can determine if any of them are roots and then use long division to factor the equation and find the remaining roots. However, this method can become tedious and may still require some basic understanding of polynomial functions.

• Calculus and Beyond Homework Help
Replies
11
Views
1K
• Calculus and Beyond Homework Help
Replies
8
Views
1K
• Differential Equations
Replies
1
Views
2K
• Math Proof Training and Practice
Replies
1
Views
2K
• Science and Math Textbooks
Replies
4
Views
1K
• Math Proof Training and Practice
Replies
1
Views
2K
• Calculus and Beyond Homework Help
Replies
1
Views
1K
• Math Proof Training and Practice
Replies
137
Views
16K
• Set Theory, Logic, Probability, Statistics
Replies
2
Views
1K
• Calculus and Beyond Homework Help
Replies
4
Views
1K