at most one root

USAGE SUMMARY

The phrase "at most one root" is correct and usable in written English.
It can be used in mathematical contexts, particularly when discussing the number of solutions to equations or functions. Example: "The quadratic equation has at most one root, indicating that it may touch the x-axis at a single point."

✓ Grammatically correct

Science

News & Media

Academia

Human-verified examples from authoritative sources

Exact Expressions

4 human-written examples

Then b can have at most one root on [ 0, 1 ].

Journal of Mathematics in Industry

If (d< c), then Q is decreasing on ((-infty,-c]), so Q has at most one root in this interval.

Journal of Inequalities and Applications

The polynomial (Q x)) is decreasing on the interval ([-a_{2},-c_{1}]), so it has at most one root in this interval.

Journal of Inequalities and Applications

Hence the equation for (c t,lt)) can have at most one root in ((0,t^{0,t^{

Journal of Inequalities and Applications

Human-verified similar examples from authoritative sources

Similar Expressions

52 human-written examples

With this tool in hand, we construct a parallel procedure for the localization and isolation of all the roots by dividing the given region successively and applying the above formula to these subregions until the final domains contain at the most one root.

Journal of Computational and Applied Mathematics

According to Descarte's rule of signs, f ( x ) = 0 has at most one positive real root.

Advances in Difference Equations

For a given tree T, we call a subset c of its nodes a coloring, if it satisfies the following two conditions: each path from a leaf to the root contains at most one node from c, each internal node in c has a sibling node which does not belong to c.

BMC Genomics

Consider a tree T and a set ℒ ′ ⊆ ℒ T. The restriction of T to ℒ ′, denoted by T | ℒ ′, is the minimal homeomorphic subtree of T connecting the leaves with labels in ℒ ′ (that is, we start with the minimal subtree of T connecting ℒ ′, and repeatedly suppress non-root nodes with at most one child until no such nodes remain).

Algorithms for Molecular Biology

Hence, the function L : ( 0, n ) → R has at most one extreme point, and L ( t ) has at most two roots in ( 0, n ).

Journal of Inequalities and Applications

Equation (5.13) at most has one real root; but is its real root, thus, and the proposition holds.

Boundary Value Problems

It is a calm familiar to most communities, one rooted in routine and summer dog days.

Los Angeles Times

Expert writing Tips

Best practice

When discussing the number of roots of a polynomial or equation, use "at most one root" to indicate that there can be either one root or no roots, clearly communicating an upper limit.

Common error

Avoid using "at most one root" when you mean there is precisely one root. "At most one root" allows for the possibility of no roots, while "exactly one root" specifies a single, unique solution.

Linguistic Context

The phrase "at most one root" functions as a quantifier in mathematical and scientific contexts. It specifies an upper limit on the number of roots an equation or function can have. As confirmed by Ludwig, it is grammatically correct.

Expression frequency: Common

Frequent in

Science

70%

Academia

20%

News & Media

10%

Less common in

Formal & Business

0%

Encyclopedias

0%

Wiki

0%

Ludwig's WRAP-UP

The phrase "at most one root" is a grammatically sound and commonly used expression, particularly within scientific and mathematical fields. According to Ludwig, it's used to define an upper limit to the number of roots a function or equation can have. Analysis of sources shows primary usage in Science and Academia, and its intent is to set conditions rather than make claims of existence. Related phrases include "no more than one root" and "a maximum of one root". When using this phrase, remember it means 'one or zero', and not 'exactly one'. This information should help in using the expression with confidence and precision.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

no more than one root

Emphasizes the upper limit, suggesting that the number of roots cannot exceed one.

a maximum of one root

Explicitly states that one is the highest possible number of roots.

up to one root

Indicates a range from zero to one root, inclusive.

one root or fewer

Clearly states the options: either one root or no roots.

at most a single root

Replaces "one" with "single" for emphasis, maintaining the same meaning.

not more than one root

A more formal way of saying "no more than one root".

one root maximum

Places "maximum" after "root" for a slightly different emphasis.

a unique root at most

Highlights the uniqueness aspect if there is only one root.

at most one solution

Broader term using "solution" instead of "root", applicable in various mathematical contexts.

no more than a solitary root

Uses more descriptive language to convey the same idea, using "solitary" to describe the root.

FAQs

How can I use "at most one root" in a sentence?

You can use "at most one root" when describing the possible number of solutions to an equation. For example, "The function f(x) has "at most one root", meaning it intersects the x-axis either once or not at all."

What is the difference between "at most one root" and "exactly one root"?

"At most one root" indicates that there can be either one root or no roots. "Exactly one root" means there is only one root, and no more or less. The first includes the possibility of zero roots, while the second does not.

What are some alternatives to saying "at most one root"?

Alternatives include "no more than one root", "a maximum of one root", or "up to one root". These phrases all convey the same meaning of an upper limit on the number of roots.

Is it grammatically correct to say "at most one root"?

Yes, the phrase "at most one root" is grammatically correct and commonly used in mathematical and scientific contexts to describe the possible number of solutions to an equation or function.