QUADRATIC EQUATION SOLUTION HOW TO
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Zero Discriminant: when b 2 вЂ“ 4ac = 0, we have one repeated real solution to the quadratic equation.Positive Discriminant: when b 2 вЂ“ 4ac > 0, we have two distinct real solutions to the quadratic equation.There are three cases for the sign of the discriminant, corresponding to the type of solutions for a quadratic equation: The discriminant of a quadratic equation is the expression under the radical symbol in the quadratic formula: b 2 вЂ“ 4ac. To find the nature of the solutions of a quadratic equation (what type of solutions we have), we can use one part of the formula: the discriminant. The expression under the radical, b 2 вЂ“ 4ac, is called the discriminant and helps us to determine the nature of the solutions of a quadratic equation.ДЄfter putting the quadratic equation into standard form, ax 2 + bx + c = 0, we can find a, b, and c to use in the quadratic formula. Remember that we can graph a quadratic function f(x) = ax 2 + bx + c as a parabola (shown below). The solutions of a quadratic equation represent the points on a graph where a parabola intersects the x-axis. What Do The Solutions Of A Quadratic Equation Represent On A Graph? They represent very specific points on the graph of a parabola. Of course, the solutions of a quadratic equation also have a visual interpretation. We can use FOIL and the Distributive Property to verify this: If we know that the roots are x = 1 and x = 2, then we can factor completely with a = 5, r = 1, and s = 2: Given the quadratic function f(x) = ax 2В + bx + c, the solutions x = r and x = s give us the complete factorization:ДЇor example, consider the quadratic function f(x) = 5x 2 -15x + 10. The solutions of a quadratic equation also represent a way for us to factor. We can verify these two solutions by substituting them for x in the quadratic function: We can see this if we factor it as a difference of squares: That is, if x = a is a solution to the quadratic function f(x), then f(a) = 0.ДЇor example, consider the quadratic function f(x) = x 2 вЂ“ 1, with solutions are x = 1 and x = -1. These x values are also called the roots of the quadratic equation. For a quadratic equation in standard form, these x values will make the left side of the equation equal to zero.ДЇor a quadratic function f(x), the solutions are the values of x that make y equal to zero. The solutions of a quadratic equation represent the values of x that make the equation true. What Do The Solutions Of A Quadratic Equation Represent? WeвЂ™ll also take a closer look at some of the cases for the solutions and when they occur. In this article, weвЂ™ll talk about the solutions of a quadratic equation and what they represent. For a quadratic function f(x), the solutions of the quadratic equation tell us when f(x) = 0. Of course, for a quadratic equation in standard form, the solutions tell us when the left side is equal to zero. Visually, the solutions of a quadratic equation represent the points where a parabola intersects the x-axis (that is, where y = 0). We can factor a quadratic equation in standard form with these solutions. So, what do the solutions of a quadratic equation represent? The solutions of a quadratic equation represent x values where the equation is true.

QUADRATIC EQUATION SOLUTION HOW TO

However, knowing how to find these solutions is not the same as knowing what they mean. It has all the questions with Important Questions also marked.You will spend a lot of time in algebra classes trying to find the solutions of quadratic equations. To open other question of the exercise, go to bottom of the page. Note: When you click on a link, the first question of the exercise will open. We suggest you do the Chapter from Concept Wise - it is the Teachoo (а¤џаҐЂа¤љаҐ‚) way of learning. First the concepts are explained, and then the questions of the topic are solved - from easy to difficult.

In Concept Wise, the chapter is divided into concepts.

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In Serial Order Wise, the chapter is divided into exercise questions and examples. This chapter is divided into two parts - Serial Order Wise, Concept Wise

Checking if roots are real, equal or no real roots (By Checking the value of D =В b 2 - 4ac).

Solving a Quadratic Equation using D Formula (x = -b В± в€љb 2 - 4ac / 2a).

Solving a Quadratic Equation by Completing the Square.

Solution of a Quadratic Equation by Factorisation ( Splitting the Middle Term method).

What is the Standard Form of a Quadratic Equation.

Answers to each and every question is provided video solutions.

QUADRATIC EQUATION SOLUTION FREE

Get NCERT Solutions for all exercise questions and examples of Chapter 4 Class 10 Quadratic Equations free at Teachoo.

Quadratic equation solution