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How can you quickly determine the number of roots a polynomial will have by looking at the equation?
Wiki User
∙ 11y ago
In the complex field, a polynomial of degree n (the highest power of the variable) has n roots. Some of these roots may be multiple roots.
However, if the domain is the real numbers (or a subset) then there is no easy way. The degree only gives the maximum number of roots - there may be no real root. For example x2 + 1 = 0.
Wiki User
∙ 11y ago
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What methods can be used to solve quadratic equations?
For any of the following methods, first make sure that all terms of the equation are on the left of the equal sign; on the right, there should only be a zero. Thus, for example, x2 - 5x = 10 becomes: x2 - 5x - 10 = 0 The methods commonly used are: 1) Factor the polynomial. Sometimes this can be done easily; but if this is too difficult, use one of the other methods below. 2) Complete the square. Add a constant term to both sides of the equation, such that the polynomial on the left becomes a perfect square. 3) Use the quadratic formula. This is usually the simplest method, if you can't find an obvious factorization quickly.
Is quickly an adverb?
Yes, quickly is an adverb. "He pedaled quickly on his bike." Quickly tells how he pedaled. It modifies the verb.
Is more quickly a proper adverb?
"More quickly" is an adverbial phrase. Quickly is an adverb.
Is quickly a verb or an adverb?
The word quickly is an adverb.The verb form would be "quicken".
How do you solve quadratic equations by factoring?
There is a new method, called Diagonal Sum Method, that quickly and directly give the 2 roots without having to factor the equation. The innovative concept of this method is finding 2 fractions knowing their sum (-b/a) and their product (c/a). It is fast, convenient and is applicable to any quadratic equation in standard form ax^2 + bx + c = 0, whenever it can be factored. If it fails to find answer, then the equation is not factorable, and consequently, the quadratic formula must be used. So, I advise you to proceed solving any quadratic equation in 2 steps. First, find out if the equation can be factored? How?. Use this new method to solve it. It usually takes fewer than 3 trials. If its fails then use the quadratic formula to solve it in the second step. See book titled:" New methods for solving quadratic equations and inequalities" (Trafford Publishing 2009)
How do you use the word equation in a sentence with an adverb?
He did that equation very quickly.
How can you find out how many solutions an equation has?
By solving it. There is no single easy way to solve all equations; different types of equations required different methods. You have to learn separately how to solve equations with integer polynomials, rational equations (where polynomials can also appear in the denominator), equations with square roots and other roots, trigonometric equations, and others.Sometimes, the knowledge of a type of equations can help you quickly guess the number of solutions. Here are a few examples. An equation like:sin(x) = 0.5has an infinite number of solutions, because the sine function is periodic. An equation with a polynomial - well, in theory, you can factor a polynomial of degree "n" into "n" linear factors, meaning the polynomial can have "n" solutions. However, it may have multiple solutions, that is, some of the factors may be equal. Also, some of the solutions may be complex. A real polynomial of odd degree has at least one real solution.By solving it. There is no single easy way to solve all equations; different types of equations required different methods. You have to learn separately how to solve equations with integer polynomials, rational equations (where polynomials can also appear in the denominator), equations with square roots and other roots, trigonometric equations, and others.Sometimes, the knowledge of a type of equations can help you quickly guess the number of solutions. Here are a few examples. An equation like:sin(x) = 0.5has an infinite number of solutions, because the sine function is periodic. An equation with a polynomial - well, in theory, you can factor a polynomial of degree "n" into "n" linear factors, meaning the polynomial can have "n" solutions. However, it may have multiple solutions, that is, some of the factors may be equal. Also, some of the solutions may be complex. A real polynomial of odd degree has at least one real solution.By solving it. There is no single easy way to solve all equations; different types of equations required different methods. You have to learn separately how to solve equations with integer polynomials, rational equations (where polynomials can also appear in the denominator), equations with square roots and other roots, trigonometric equations, and others.Sometimes, the knowledge of a type of equations can help you quickly guess the number of solutions. Here are a few examples. An equation like:sin(x) = 0.5has an infinite number of solutions, because the sine function is periodic. An equation with a polynomial - well, in theory, you can factor a polynomial of degree "n" into "n" linear factors, meaning the polynomial can have "n" solutions. However, it may have multiple solutions, that is, some of the factors may be equal. Also, some of the solutions may be complex. A real polynomial of odd degree has at least one real solution.By solving it. There is no single easy way to solve all equations; different types of equations required different methods. You have to learn separately how to solve equations with integer polynomials, rational equations (where polynomials can also appear in the denominator), equations with square roots and other roots, trigonometric equations, and others.Sometimes, the knowledge of a type of equations can help you quickly guess the number of solutions. Here are a few examples. An equation like:sin(x) = 0.5has an infinite number of solutions, because the sine function is periodic. An equation with a polynomial - well, in theory, you can factor a polynomial of degree "n" into "n" linear factors, meaning the polynomial can have "n" solutions. However, it may have multiple solutions, that is, some of the factors may be equal. Also, some of the solutions may be complex. A real polynomial of odd degree has at least one real solution.
What factors determine how quickly things melt?
Temperature and Pressure
You can determine quickly the effect of adding poles and zeros by?
Root locus
What methods can be used to solve quadratic equations?
For any of the following methods, first make sure that all terms of the equation are on the left of the equal sign; on the right, there should only be a zero. Thus, for example, x2 - 5x = 10 becomes: x2 - 5x - 10 = 0 The methods commonly used are: 1) Factor the polynomial. Sometimes this can be done easily; but if this is too difficult, use one of the other methods below. 2) Complete the square. Add a constant term to both sides of the equation, such that the polynomial on the left becomes a perfect square. 3) Use the quadratic formula. This is usually the simplest method, if you can't find an obvious factorization quickly.
When he looks at you i look back then he quickly looks down?
It means that he was looking at you but didn't want you to know that he was looking at you.
How much does the average leg exercise equipment piece cost now?
If you are simply looking for some free weights and a bench, this can be purchased for a very low price. However, if you are looking for an Olympic, LifeFitness or Bowflex machine, the price can escalate very, very quickly. First determine what your needs are, then look to purchase the equipment.
How is Einstein's equation important to the Big Bang Theory?
Einstein's equation demonstrated that some of the energy released when the universe began was quickly turned into matter, the first matter in the universe.
How do you get to prestige 10 on modern warfare quickly?
There is no quick way. It takes time, although a player's skill can determine how quickly they will get there. But believe me, it doesn't happen overnight.
What to do when you fart really loud and everyone is looking at you?
Looking downward and behind you, say "Bad dog!" and leave the scene quickly.
What is Q-Sort scale?
this determine very quickly among a reletively large number of objects .
What is the ability to size up a situation quickly determine what is important and decide what needs to be done?
judgement
