Any algebra experts?

My question is: is there any algebraic way to find the largest positive real root or the smallest negative real root of a function without graphing it Edit: I was asked to do so using newton's numerical method or secant's but any solution to clear it out would be helpful (algebraic solution)

#Algebra

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Comments

infinity squared?

Pigeon Mathlete - 2 years, 6 months ago

What??

Ahmed Mahmoud - 2 years, 6 months ago

I can see why you would want to do it analytically, but why would you want to do it algebraically? Most algebra is done over arbitrary fields or rings, for which the majority of the time there is no ordering structure. Thus, it does not make sense to talk about the "largest positive real root" or the "smallest negative real root", whatever that all means. To put it bluntly, such a question isn't something that is delved into in the realm of algebra. There is a reason why the "Fundamental Theorem of Algebra" is a misnomer for something much more complicated.

A Former Brilliant Member - 2 years, 6 months ago

I just wanted to know if there is a specific property of largest positive real root or smallest negative real root which helps to get them algebraicly not just by setting some arbitary large interval and hope the answer exists in it but it seems that there isn't

Ahmed Mahmoud - 2 years, 6 months ago

Thanks for your reply ☺️☺️

Ahmed Mahmoud - 2 years, 6 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$