Therefore, the product of the numbers we choose should be equal to -3 (-1*3). In these cases, we multiply the constant c with the coefficient of x 2. Rewriting our equation, we get 3x 2+2x-1= 0
Quadratic polynomial example how to#
Let us see how to solve the equations where the coefficient of x 2 is greater than 1. The numbers which add up to -18 and give +45 when multiplied are -15 and -3.
Let us express -3x as a sum of -5x and +2x. Let us solve some more examples using this method. The roots of this equation -2 and -3 when added give -5 and when multiplied give 6. Sum of the roots for the equation x 2+5x+6 = 0 is -5 and the product of the roots is 6. We saw earlier that the sum of the roots is –b/a and the product of the roots is c/a. Let us express the middle term as an addition of 2x and 3x. We have to take two numbers adding which we get 5 and multiplying which we get 6. Now, let’s calculate the roots of an equation x 2+5x+6 = 0. Here, a and b are called the roots of the given quadratic equation. The sum of its roots = –b/a and the product of its roots = c/a.Ī quadratic equation may be expressed as a product of two binomials.įor example, consider the following equation These are called the roots of the quadratic equation. The following are examples of some quadratic equations:įor every quadratic equation, there can be one or more than one solution. In this article we cover quadratic equations – definitions, formats, solved problems and sample questions for practice.Ī quadratic equation is a polynomial whose highest power is the square of a variable (x 2, y 2 etc.) DefinitionsĪ monomial is an algebraic expression with only one term in it.Ī polynomial is an algebraic expression with more than one term in it.Ī polynomial is formed by adding/subtracting multiple monomials.Įxample: x 3+2y 2+6x+10, 3x 2+2x-1, 7y-2 etc.Ī polynomial that contains two terms is called a binomial expression.Ī polynomial that contains three terms is called a trinomial expression.Ī standard quadratic equation looks like this:Ī, b are called the coefficients of x 2 and x respectively and c is called the constant.
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