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

[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!

 

[Mark44]

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?

, 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.