Solution of a Quadratic Equations

Simon Stevin discovered the quadratic formula. The term “quadratic” is derived from the word “quad,” which means square. This means that the greatest power term in the quadratic equation is a variable raised to 2. A quadratic equation’s standard form is given by the equation ax2+bx+c=0 where, a≠0 We know that any value(s) of x that satisfy the equation is referred to as a solution (or) root of the equation, and the process of determining the values of x that satisfy the equation ax2+bx+c=0  is referred to as solving quadratic equations. Quadratic functions have a special place in the school curriculum. They are functions whose values can be easily calculated from input values, so they are a slight improvement over linear functions and represent a significant departure from the attachment to straight lines.

Solution of a Quadratic Equations

In mathematics, a quadratic equation is defined as an equation of degree 2, which means that the highest exponent of this function is 2. A quadratic has the standard form y=ax^ 2+bx+c

 Where a,b, and c are numbers and a cannot be zero. All of these are examples of quadratic equations: 

y=x^ 2+3x+1.y=x^  2

How to find the Solution of a Quadratic Equations

Solving quadratic equations entails determining a variable value (or values) that satisfy the equation. The value(s) that satisfy the quadratic equation are referred to as the root solutions 0. Because the degree of the quadratic equation is two, it can only have two roots.

 For example,

x=1 & x=2  Easily satisfy the quadratic equation x²-3x+2=0

 You can substitute each of the values in this equation and verify.

 Thus, the roots of x²-3x+2=0 are x=1 & x=2  

There are different ways of solving quadratic equations.

• Factoring quadratic equations to solve them
• Completing the square to solve quadratic equations
• Graphing quadratic equations to solve them
• Using the quadratic formula to solve quadratic equations

Aside from these methods, there are a few others that are only used in certain situations (when the quadratic equation has missing terms), as explained below.

Factoring quadratic equations

Factoring quadratic equations is a very good method for solving quadratic equations. An example is provided to demonstrate the step-by-step process of factoring quadratic equations.

Where the equation x²-3x+2=0  will be solved

1st step: Convert the equation to standard form. i.e., get all the terms of the equation to one side (usually the left side) so that the other side is 0.

The equation x²-3x+2=0  has already been written in standard form.

2nd step: Factor the quadratic expression. Click here to learn how to factor a quadratic expression.

The result isx-1x-2=0

3rd step: Using the zero product property, set each factor to zero. 

x-2=0

4th step: Solve each of the preceding equations.

x=1 OR x=2

As a result, the quadratic equation  x²-3x+2=0 has solutions 1 and 2. This method is only applicable when the quadratic expression can be factored. If it is NOT factorable, we can use one of the other methods described below. Similar to quadratic equations, linear equations have solutions that are used to solve linear programming problems.

Formula to find Solution of a Quadratic Equations

We can use the quadratic formula to solve any quadratic equation. To begin, we simplify the equation ax²-bx+c=0 , where a, b, and c are coefficients. The coefficients are then entered into the formula:

Quadratic Formula 

x = -b ± √b² – 4ac/2a     

Conclusion

Simon Stevin discovered the quadratic formula. The term “quadratic” is derived from the word “quad,” which means “square. In the school curriculum Quadratic functions have a special place. Functions whose values can be easily calculated from input values, so they are a slight improvement over linear functions and represent a significant departure from the attachment to straight lines.