Solving Quadratic Equations – Use Algebra Calculator

Algebra is one of the important parts of mathematics, and it is right to say it is an essential branch of mathematics. Algebra includes three common parts in their equation such as unknown parts which are known as variable, coefficient and number values. According to the degree available in the unknown part, the algebra is known as a different name such as a linear equation, polynomial equation, quadratic equation, cubic equation, exponential equation and much more. Thus, the algebra is a large part of mathematics. Here we are going to learn solving quadratic equations in different methods.

About quadratic equation

It is one of the algebraic equation which includes two factors or roots of unknown value. If learn simply, the standard format of quadratic equation is-

ax² + bx + c = 0

Here the standard format of a quadratic equation is visible where you can find variable (x), constant or number term (c) and coefficient of x²  and x i.e. a and b.

Now solving the quadratic equation is quite simple with the latest algebra calculators but slightly difficult if solved by formula methods. Different methods you can use to solve the quadratic equations in which formula method is explained below in the content.

Consider an example to learn how to solve quadratic equation by formula method

x² + 3x – 4 = 0

Formula to identify the unknown term is: -b ± √b²-4ac⁄2a

According to the standard format of quadratic equation a = 1, b = 3 and c = -4

Put these values on the formula to find the value of a variable. You will get,

x = -3 ± √9 – 4.1. (-4)⁄2.1

x = -3 ± √9+16⁄2

x = -3 ± √25⁄2

x = -3 ± 5⁄2

Now, you can consider mathematical signs separately to identify both values separately that can balance the whole equation. Follow steps given below-

x = -3 + 5⁄2

x = 2⁄2

x = 1

And,

x = – 3 – 5⁄2

x = – 8⁄2

x = – 4

Now, you have two separate values of variable, i.e. x=1 and-4

This is formula method to solve any quadratic equation. It is quite simple, but you have to perform a much mathematical operation like multiplication, division, subtraction, and addition too. Also, you use other methods for solving a quadratic equation. In the quadratic equation, there are two roots are available that can balance the whole equation. Consider the same example to learn the root method of solving quadratic equations.  x² + 3x – 4 = 0

Here a = 1, b = 3 and c = – 4

To find out the variable values, use particular formula as-

α + β = – b⁄a

α β = c⁄a

Put the values to get the values of α and β

α + β = – 3⁄1

α + β = – 3

And

α β = -4⁄1

α β = – 4

Square both the term of ∝+β to find out unknown values as

α² + β² + 2αβ = 9

Now,

(α – β) ² + 2αβ + 22 αβ = 9

(α – β) ² + 2αβ + 22αβ = 9

(α – β) ² + 4αβ = 9

Put the values of α β in the above equation

(α – β) ² + 4 * – 4 = 9

(α – β) ² – 16 = 9

(α – β) ² = 25

α – β = 5

 

Now add α – β and α + β

You will get

2α = 2

Then

α = 1

Put the value of ∝ in any above equation

You will get

β = -4

Hence, you have a choice to use different methods to solve a quadratic equation. On the other hand, you can choose the algebra calculator that can easily find out variable values and deliver results in fast. In the algebra calculator, you just need to enter the quadratic equitation on the required field in the calculator. Thus, enter one next tap to solve the equation. The calculator solves the equation with the genuine method, and there is no short answer you will get. Thus, solving quadratic equations is quite easy with the calculator.

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When Quadratic Formula is Used

With elementary algebra, quadratic formula is used for the solution of a quadratic equation. You can find many ways that you can use to solve this problem without using the quadratic formula like graphing, completion of the square or factoring while using the quadratic formula maybe most convenient method. The quadratic equation looks like ax2+bx+c=0.  With this equation, x stands for unknown but a, b, with C should be constant, and A should not be zero. Someone may verify that the quadratic formula does satisfy quadratic equation through inserting the first number in the last number.

quadratic formula
quadratic formula

The solution found with the quadratic formula is known as the root for a quadratic equation.  In geometry, such roots can represent the value of x which is the parabola given will cross at the axis of X. The formula can yield zero of different parabola while quadratic formula can give axis to the symmetry of a parabola. This is normally used in order to determine the number of the zero which the quadratic equation does have.

The formula may get derived from the simple application with a technique application needed to complete a square. This is why; a derivation can be sometime left like the exercise of the students who wish to experience the rediscovery of the formula.

A quadratic equation can be in the form to complete a square when it is applied. You may add the constant on the two sides of an equation like the left-hand side which become the complete square.  The terms should be rearranged at a right-hand side so that we can obtain the common denominator. When the square had been completed, then the square root of the two sides have to be found and then isolating the x to get the quadratic formula.

The solution of a quadratic equation can be gotten by using different alternatives of the derivation with the minor differences, and this is through manipulating a. Some of the old sources may use the alternative of parameterization for the equation by using b with a magnitude of the half of a common number.  Even if the results can be different from the first solution, however, they are also equivalent.

Without the need to go in the parabolas like the geometrical objects of the cone, the parabola will be the curve which is being described as the second degree of the polynomial.

The early method to solve the quadratic equation was done in the geometry.   The Babylonian cuneiform tablet had the problems that are reducible in solving a quadratic equation. Egyptian Berlin Papyrus that dated back in the middle kingdom had some solution for a two-term equation.   In Greek, the mathematician Euclid was using the geometric method in order to solve the quadratic equation in the Elements Book 2.  The laws of the quadratic equation do appear in Nine Chapters on Mathematical Art circa from China. A Greek mathematician Diophantus in the work he did on the arthmetica, he solved some quadratic equations which are recognizable to the algebraic done by Euclid. The solution he used was able to give one root, regardless if positive roots were used.