As a student, there’s one thing you’ll eventually want to be able to do: solve a quadratic equation. It’s not hard, but it can seem daunting at first. The good news is that with a few simple steps, you’ll be able to breeze through this math problem like a pro. So without further ado, let’s get started!
The goal of this blog post is twofold: (1) To provide an easy-to-follow guide on how to solve a quadratic equation and (2) To help dissolve any fears or doubts about solving quadratics that students may have. After reading this post, students will feel confident in their ability to tackle any linear equation head-on!
Definition of Quadratic Equation
A quadratic equation is a mathematical equation that can be written in the form of ax^2 + bx + c = 0, where x represents an unknown variable, and a, b, and c represent known coefficients. This equation typically has two solutions, or roots, which can be positive or negative values. The value of x that satisfies the equation is known as the Quadratic Formula.
The quadratic equation has many applications in mathematics and physics. For example, it can be used to calculate the path of a projectile under the influence of gravity or to determine the equilibrium point of a structure that is subject to external forces. In addition, the quadratic equation can be used to solve for the unknown side length of a triangle when two other side lengths are known.
Quadratic Equation Examples
Do you struggle with solving quadratic equations? Do you feel like you never quite understand what the steps are supposed to be? Well, don’t worry- you’re not alone. Many students find quadratic equations difficult to master. But don’t give up! With a little bit of practice, and some helpful examples, you can definitely get the hang of it. Here are some Quadratic equation examples,
6x² + 11x – 35 = 0.
2x² – 4x – 2 = 0.
-4x² – 7x +12 = 0.
20x² -15x – 10 = 0.
x² -x – 3 = 0.
5x² – 2x – 9 = 0.
3x² + 4x + 2 = 0.
-x² +6x + 18 = 0.
How to Solve a Quadratic Equation?
Quadratic equations can be tricky, but with a little bit of practice, you’ll be able to solve them like a pro. So sit back and relax while we take you through the steps. You’ll be amazed at how easy it is! Here are three ways to solve Quadratic Equations
Factorization
Factorization is the process of expressing a number or an expression as a product of its factors. In other words, it is the process of finding all the factors of a given number or expression. There are two methods to factorize an expression: common factor method and grouping method.
The common factor method is used when there are two or more terms with a common factor. The grouping method is used when there are three or more terms with no common factors. To solve a quadratic equation using the factorization method, we need to first identify the factors of the constant term and then identify the factors of the coefficient of the x^2 term. Once we have these factors, we can set each factor equal to zero and solve for x.
For example, consider the equation x2 + 5x + 6 = 0. The constant term is 6 and the coefficient of the x2 term is 1. The factors of 6 are 1, 2, 3, and 6. The only pair of factors that add up to 5 is 1 and 6. So, we can rewrite this equation as (x+1)(x+6) = 0. Setting each factor equal to zero and solving for x gives us x = -1 and x = -6 as our solutions.
Completing Square
Completing the square is a process that can be used to solve certain types of quadratic equations. The general form of a quadratic equation is ax2+bx+c=0. To solve a quadratic equation using the completing the square method, we need to first rearrange the equation into what is known as the standard form.
The standard form of a quadratic equation is ax2+bx=c. Once the equation is in this form, we can then complete the square on both sides of the equation. This means that we need to add a number to both sides of the equation such that when we take the square root of both sides, we are left with a perfect square.
Quadratic Formula
The quadratic formula is a mathematical formula used to solve quadratic equations. A quadratic equation is an equation where the highest power of the variable is 2. The quadratic formula can be used to find the roots of any quadratic equation, provided that the equation is in standard form. The standard form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are real numbers and x is the variable. To use the quadratic formula, simply substitute the values of a, b, and c into the formula and solve for x.
x=-bb2-4ac2a
The quadratic formula is especially useful when solving problems that involve finding the vertex of a parabola or the turning point of a curve. In addition, the quadratic formula can be used to calculate the area of a triangle whose two sides are intersected by a parabola. Overall, the quadratic formula is a powerful tool that can be used to solve many different types of equations.
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MATHS Related Links |
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| Arithmetic Mean | |
| Law of Trichotomy | |
| Remainder Theorem | Null Matrices |
| Properties of real numbers | |
Conclusion
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