Algebraic Equation Solver

Polynomial Equation Polynomial Equation In mathematics, a polynomial is an expression of finite length constructed from variables (also known as indeterminates) and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents. For example, x2 â&#x2C6;&#x2019; x/4 + 7 is a polynomial, but x2 â&#x2C6;&#x2019; 4/x + 7x3/2 is not, because its second term involves division by the variable x (4/x) and because its third term contains an exponent that is not an integer (3/2). The term "polynomial" can also be used as an adjective, for quantities that can be expressed as a polynomial of some parameter, as in polynomial time, which is used in computational complexity theory. Polynomial comes from the Greek poly, "many" and medieval Latin binomium, "binomial".The word was introduced in Latin by Franciscus Vieta. Polynomials appear in a wide variety of areas of mathematics and science. For example, they are used to form polynomial equations, which encode a wide range of problems, from elementary word problems to complicated problems in the sciences. Know More About Critical Values of T Math.Tutorvista.com

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They are used to define polynomial functions, which appear in settings ranging from basic chemistry and physics to economics and social science; they are used in calculus and numerical analysis to approximate other functions. In advanced mathematics, polynomials are used to construct polynomial rings, a central concept in abstract algebra and algebraic geometry Example : Solve \frac{3x^2-1}{2}+\frac{2x+1}{3} = \frac{x^2-2}{4} + \frac{1}{3} Solution : Step 1: Eliminate fractions by multiplying each side by the least common denominator. In this example we multiply both sides by 12. \begin{aligned} \frac{3x^2-1}{2}+\frac{2x+1}{3} & = \frac{x^2-2}{4} + \frac{1}{3} \\ {\color{red} {12}}\cdot\frac{3x^2-1}{2}+{\color{red}{12}}\cdot\frac{2x+1}{3} & = {\color{red} {12}}\cdot\frac{x^2-2}{4} + {\color{red}{12}}\cdot\frac{1}{3}\\ 6\cdot(3x^2-1)+4\cdot(2x+1) & = 3\cdot(x^2-2) + 4 \end{aligned} Step 2:Simplify each side by clearing parentheses and combining like terms. \begin{aligned} 6\cdot(3x^2-1)+4\cdot(2x+1) & = 3\cdot(x^2-2) + 4 \\ 18x^2-6+8x+4 & = 3x^26+4\\ 18x^2+8x-2 & = 3x^2-2\\ \end{aligned} Step 3:Use the addition property to get all terms on one side of the equation. \begin{aligned} 18x^2+8x-2 & = {\color{red}{3x^2-2}}\\ 18x^2+8x-2{\color{red}{-3x^2+2}} & = 0\\ 15x^2+8x & = 0 \end{aligned} Step 4:Finally, solve the equation. Here we have second degree equation so you can use step-by-step quadratic equation solver to find the solutions : {\color{blue}{ x_1 = 0, x_2 = -\frac{8}{15} }} If you have an equation of higher degree then you can use polynomial roots calculator. Unfortunately, this calculator will show you the solution, but without explanation. Learn More Partial Differentiation Math.Tutorvista.com

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Algebra homework help Algebra homework help Learning algebra is a little like learning another language. In fact, algebra is a simple language, used to create mathematical models of real-world situations and to handle problems that we can't solve using just arithmetic. Rather than using words, algebra uses symbols to make statements about things. In algebra, we often use letters to represent numbers. Since algebra uses the same symbols as arithmetic for adding, subtracting, multiplying and dividing, you're already familiar with the basic vocabulary. In this lesson, you'll learn some important new vocabulary words, and you'll see how to translate from plain English to the "language" of algebra. The first step in learning to "speak algebra" is learning the definitions of the most commonly used words. Algebraic Expressions : An algebraic expression is one or more algebraic terms in a phrase. It can include variables, constants, and operating symbols, such as plus and minus signs. It's only a phrase, not the whole sentence, so it doesn't include an equal sign.

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Algebraic expression: 3x2 + 2y + 7xy + 5 In an algebraic expression, terms are the elements separated by the plus or minus signs. This example has four terms, 3x2, 2y, 7xy, and 5. Terms may consist of variables and coefficients, or constants. Variables :- In algebraic expressions, letters represent variables. These letters are actually numbers in disguise. In this expression, the variables are x and y. We call these letters "variables" because the numbers they represent can varyâ&#x20AC;&#x201D;that is, we can substitute one or more numbers for the letters in the expression. Coefficients :- Coefficients are the number part of the terms with variables. In 3x2 + 2y + 7xy + 5, the coefficient of the first term is 3. The coefficient of the second term is 2, and the coefficient of the third term is 7. If a term consists of only variables, its coefficient is 1. Constants :- Constants are the terms in the algebraic expression that contain only numbers. That is, they're the terms without variables. We call them constants because their value never changes, since there are no variables in the term that can change its value. In the expression 7x2 + 3xy + 8 the constant term is "8." Real Numbers :- In algebra, we work with the set of real numbers, which we can model using a number line.