what are roots in an equation?
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Roots are also called x-intercepts or zeros. ... The roots of a function are the x-intercepts. By definition, the y-coordinate of points lying on the x-axis is zero. Therefore, to find the roots of a quadratic function, we set f (x) = 0, and solve the equation, ax2 + bx + c = 0.
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The roots of a quadratic equation simply tell what values of x will make the equation true. A quadratic function is a function where the largest power for the variable is 2. A function usually takes the form of y = or f(x) =. ... A quadratic expression is usually just something that can be simplified or factored.
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The solutions of the quadratic equation ax2 + bx + c = 0 correspond to the roots of the function f(x) = ax2 + bx + c, since they are the values of x for which f(x) = 0.
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If the discriminant is greater than zero, this means that the quadratic equation has two real, distinct (different) roots. x2 - 5x + 2. If the discriminant is greater than zero, this means that the quadratic equation has no real roots. Therefore, there are no real roots to the quadratic equation 3x2 + 2x + 1.
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By definition, the y-coordinate of points lying on the x-axis is zero. Therefore, to find the roots of a quadratic function, we set f (x) = 0, and solve the equation, ax2 + bx + c = 0. 1.
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Expressions and Equations. An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An equation is made up of two expressions connected by an equal sign.
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For an equation to be a polynomial, the power of the independent or "x" variable of each term must be a whole number. The terms can be made up of constants and variables. If the equation is not a polynomial, it is not a linear equation. In the example, y = 7/5 - (6/5)x has one "x" term and its power is 1.
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Algebraic equation. ... Algebraic equation, statement of the equality of two expressions formulated by applying to a set of variables the algebraic operations, namely, addition, subtraction, multiplication, division, raising to a power, and extraction of a root. Examples are x3 + 1 and (y4x2 + 2xy – y)/(x – 1) = 12.
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If the discriminant is equal to zero, this means that the quadratic equation has two real, identical roots. Therefore, there are two real, identical roots to the quadratic equation x2 + 2x + 1. D > 0 means two real, distinct roots.
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The correct answer is m = −8 or 3. You can find the solutions, or roots, of quadratic equations by setting one side equal to zero, factoring the polynomial, and then applying the Zero Product Property. The Principle of Zero Products states that if ab = 0, then either a = 0 or b = 0, or both a and b are 0.
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In mathematics, an algebraic equation or polynomial equation is an equation of the form. where P is a polynomial with coefficients in some field, often the field of the rational numbers. For most authors, an algebraic equation is univariate, which means that it involves only one variable.
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10 Answers. An equation is any expression with an equals sign, so your example is by definition an equation. Equations appear frequently in mathematics because mathematicians love to use equal signs. A formula is a set of instructions for creating a desired result.
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In algebra, an equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value. The most basic and common algebraic equations in math consist of one or more variables.
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A root is a value for which a given function equals zero. When that function is plotted on a graph, the roots are points where the function crosses the x-axis. For a function, f(x) , the roots are the values of x for which f(x)=0 f ( x ) = 0 .
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Factoring is a step taken towards solving a quadratic equation. ... You cannot factor them, the only way to find the roots then, is by using the quadratic formula. Suppose you factor the quadratic polynomial as and . Then set them equal to zero and solve for , you will have and .
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Equivalent equations are algebraic equations that have identical solutions or roots. Adding or subtracting the same number or expression to both sides of an equation produces an equivalent equation. Multiplying or dividing both sides of an equation by the same non-zero number produces an equivalent equation.
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We will learn the formation of the quadratic equation whose roots are given. To form a quadratic equation, let α and β be the two roots. Let us assume that the required equation be ax2 + bx + c = 0 (a ≠ 0). According to the problem, roots of this equation are α and β.