Quadratic Equation

Hey Guys!!! Are you looking for the 9th Grade Quadratic Equations Math Solutions? This is the best place for the students to know deeply about the concept of quadratic equations. There are a lot of advantages to following our page. Here we provide different methods to solve the problems in Quadratic Equations. It helps to enhance your knowledge of polynomials. All types of solve problems on different topics are explained in detail here. In this chapter, the students can find a lot of examples of solving quadratic equations with answers.

Quadratic Equations

It is very important for the students to go through the topics before they start preparing the problems. The topics covered in this chapter are the formation of quadratic equations in one variable, properties of quadratic equation, Roots of quadratic equation, methods of solving quadratic equations, etc. Refer to the topics given below and start practicing the problems of any topic as you wish. You can find Word Problems, Worksheets on quadratic equations by factoring from here. Click on the below links and make your preparation better.

Introduction to Quadratic Equation

The quadratic equation or second-degree equation is an algebraic expression of the 2nd degree in variable x. The variable x has two answers real or complex numbers. The answers or solutions of x are called roots of the quadratic equations. They are specified as (α, β). The two roots of the quadratic equation help to find the sum and products of the roots of the Q.E.

The standard form of the quadratic equation is ax² + bx + c = 0.
Where a, b is the coefficient of x² and c is the constant.
a,b, c are not fractions nor decimals.

Formation of Quadratic Equation in One Variable

Quadratic Equation in One Variable is an equation in which the variable changes to a degree of 2 is a quadratic equation. We know that quadratic is related to a square. An equation in which the variable has a maximal degree of two is a quadratic one. Let us learn deeply about the formation of quadratic equations in one variable with examples from this article.

Standard Form of the Quadratic Equation

The standard form of the quadratic equation is ax² + bx + c = 0. The graph of the quadratic equation is shown below. It is observed that the graph of a quadratic equation is a parabola.

quadratic equation

General Properties of Quadratic Equation

Students of Grade 9 can learn more about the properties of the quadratic equations with questions and answers from this page. The general form of the quadratic equation is ax² + bx + c = 0.

  1. It has in C two roots since the imaginary numbers form an algebraically closed field containing the coefficients.
  2. The sum of the roots is -b/a.
  3. The product of the roots is c/a.

Methods of Solving Quadratic Equations

There are three methods for solving quadratic equations.
1. Factorization Method:
The main aim of this method is the principle of zero products. If the product of two roots is zero, then at least one of the factors is 0. The sum of the roots of the quadratic equation is b/a, the product of the roots is c/a.
The quadratic equation is ax² + (Sum of the roots) x + Product of the roots = 0

2. Method of perfect square:
The standard form of the quadratic equation is ax² + bx + c = 0.
Divide both sides by a to make the quadratic equation into a perfect square. Solve the terms to find the roots of the variable.

3. Using Quadratic Formula:
The third method to find the roots of the quadratic equation is by using the formula.
(α, β) = [-b ± √(b² – 4ac)]/2a

Roots of a Quadratic Equation

The roots of the quadratic equation are denoted by alpha and beta. The nature of the roots of the quadratic equations is also called zero of the equation. Let us learn about the nature of the roots of the quadratic equation from here.

  • The discriminant of the quadratic equation is D = b² – 4ac.
  • For the case, D = 0 the roots are real and equal.
  • For the case, D > 0 the roots are real and distinct.
  • For the case, D < 0 the roots do not exist, or the roots are complex.

Tricks for Solving Quadratic Equations

There are some tricks to solve quadratic equations easily.
1. Generally the quadratic equations are solved by using the formula, perfect square, and factorization method.
2. The roots of the quadratic equation are called zeros of the equation.
3. The sum of the roots and product of the roots of a quadratic equation can be used for finding the higher algebraic expressions.

FAQs on Quadratic Equations

1. Where can I find the problems of quadratic equations?

Students can get the solved examples of all the topics of quadratic equations on eurekamathanswers.com

2. What are three general forms of quadratic equations?

The three general forms of the quadratic equations are standard form, factored form, and vertex form.

3. What is the other name of the quadratic equation?

As the quadratic equation involves one unknown value it is called univariate. The quadratic equation contains only powers of x that are non-negative integers and is thus known as the polynomial equation.

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