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A distinct root refers to a solution of an equation that is unique and not repeated. In the context of polynomial equations, a distinct root means that the root has a multiplicity of one, indicating it only appears once in the factorization of the polynomial. For example, in the polynomial ( f(x) = (x - 2)(x - 3)^2 ), the root ( x = 2 ) is a distinct root, while ( x = 3 ) is not, as it has a multiplicity of two. Distinct roots are important in various mathematical contexts, including algebra and calculus, as they indicate the points where a function intersects the x-axis.
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Why the quadratic equation has only one distinct solution?
A quadratic equation has only one distinct solution when its discriminant (the part of the equation under the square root in the quadratic formula) is zero. This occurs when the equation can be expressed in the form ( (x - r)^2 = 0 ), where ( r ) is the repeated root. In this case, the parabola touches the x-axis at a single point, indicating that there is only one unique solution. Thus, the equation has a double root, rather than two distinct solutions.
How can we distinguish between the main part of a root?
The main part of a root, known as the root system, can be distinguished by its primary functions: anchoring the plant, absorbing water and nutrients, and storing energy. Morphologically, the main root (often a taproot in dicots or fibrous roots in monocots) is typically thicker and longer than lateral roots, which branch off from it. Additionally, the main root usually exhibits a distinct growth pattern and may be identifiable by its position in the soil, often reaching deeper than secondary roots. Observing these characteristics can help differentiate the main root from its branches.
What is the root of unique?
The root of the word "unique" is the Latin word "unicus," which means "single" or "one." This Latin term combines "unus," meaning "one," with the suffix "-icus," indicating a characteristic. Over time, "unique" evolved in English to describe something that is one of a kind or distinct from others.
What are the distinct fourth root of -1?
The four roots are cos(theta)+i*sin(theta) where theta = pi/4, 3*pi/4, 5*pi/4 and 7*pi/4.
How many distinct ordered arrangements can be made with the letters of mississippi?
There are 34650 distinct orders.There are 34650 distinct orders.There are 34650 distinct orders.There are 34650 distinct orders.
What is the root noun of indistict?
The root noun of "indistict" is "distinct." "Distinct" means something that is clear, separate, or easily distinguishable from others.
What is The root noun of the adjective indistinct?
The root noun of the adjective "indistinct" is "distinct."
What is the root word of indistinct?
Indistinct does not have a root noun because the word distinct is an adjective. However, the word distinct can be used as a noun by adding the suffix -ness to form the word distinctness.
What is the root noun of the word Indistinct?
The root noun of the word "indistinct" is "distinct," which means clear, easily perceived, or sharply defined.
What is the homophone for root and threw?
The homophone for "root" is "route," which sounds the same but has a different meaning. Similarly, the homophone for "threw" is "through," which is pronounced the same but has a distinct definition.
How many x-intercepts does a quartic polynomial function having 4 distinct real roots have?
Each distinct real root is an x-intercept. So the answer is 4.
What is a modified under ground stem?
A portion of a root swells for food or water storage, e.g. sweet potato. A type of storage root distinct from taproot.
What is galanga in tagalog?
"Galanga" in Tagalog is "galangan." It is a root crop used in cooking for its distinct flavor and aroma.
What gives root beer ts distinct flavor?
The answer to 'what gives rootbeer its distinct flavor' is of course, the roots of a birch plant. Plant! Not tree! Rootbeer is often called Birch Beer because of this. I hope this helped!
Is the square root of 289 a rational number?
Yes. Sort of. Actually, a positive square root has two distinct solutions, Therefore, sqrt(289) is technically two rational numbers, 17 and -17.
What was the root language of Italian?
The root language of Italian is Latin, which was spoken by the ancient Romans. Over time, Latin evolved into various local dialects, eventually leading to the development of Italian as a distinct language.
What is tagalog of galangal?
The Tagalog term for galangal is "langkawas" or "bañga." It is a type of root crop commonly used in Filipino cuisine for its distinct flavor.
