While growing up some of us had fear of algebra. However, maybe perspective plays a big role. In this article, we will try to take a look at different possibilities while working on algebra. We will try how to solve a quadric equation them and form them. Before doing that let’s learn what a quadric equation is.
The word quad originated from the square. The standard form of the quadric equation is ax² + bx + c = 0, where a and b are ≠ 0 and variable and c is a constant. The process where we try to find the value of ‘x’ is what the quadric equation is all about. We have attempted to solve quadric equations in different and standard methods within this article. Please bear with us and keep learning.
Table of Contents
- How to Solve Quadric Equations Using the Quadratic Formula
- How to Solve Quadric Equations Using Factoring Method
- Last word
How to Solve Quadric Equations Using the Quadratic Formula
You already know that the standard formation is ax²+bx+c =0 where a, b, and c are known numbers and the x is what we need to find. The values of x satisfy the equation. The quadratic equation is as follows Formula.
Let us take an example of a quadric equation first.
3x²+5x = 7, It’s a quadric equation, how to solve a quadric equation is what we will learn.
Step 1: Arrange the Quadric equation
Observe it. Let’s learn if it’s a quadric equation or not. Yes, it is. Now move the terms to one side of the equation. It may be the right side or the left side. Remember one side will be with the all-linear coefficients and constant numbers and the other side will divide with 0. For example,
Also, note that the coefficients and constant numbers should be organized in decreasing order. Like we have did.
Step 2: Identify the Values of Coefficients and Constants
Identify the values. The coefficients and constants have some or different values. For reference, the co-efficient of x² is ‘a’ and for x² it’s ‘b’. For the equation, we have let’s find out the values.
Therefore a=3, b=5, c = -7
Step 3: Put in the Values within the Quadric Formula
Start putting in the numbers of a, b, and c following the quadric formula.
We know the values of three variables beforehand. Place them carefully like we did.
Step 4: Figure out the Math and Calculate
Now we have our equation in front of our eyes. Numbers have replaced it and how to solve a quadric equation it is just one calculation away. Take good care of positive and negative numbers.
Multiply and plus-minus as required. Take extra care of the root. It could be a little tricky. First, calculate the variables between the roots. After you get the answer. Root the answer.
Now solve the root
Step 5: Separate the Positive and Negative Equations
Now we have to figure out the positive and negative equations. For that separate the positive and negative with the root on. Let’s suppose we have to find X¹ and X². Separate the two solutions.
Step 6: Solve the Math to Get the Value of X
Just do the math. Solve the different values. But keep in mind the plus and minus. Be careful. You will get the answer for one it will be in plus and for the another, it will be minus.
How to Solve Quadric Equations Using Factoring Method
You can worry abouthow to solve a quadric equation it is of no worry I assure you. Quadric equations are polynomial equations of 2 degrees. The variable type is f(x)=ax²+bx+c=0 a, b, c is variable constant and a≠0. The equation must have two roots.
Move the terms to the left or right the equation should be like this ax²+bx+c = 0. The right side with the coefficient and the left will be 0. The x² term will be positive.
Here is how you should do it: 3x²-5x+2 =0
Step 1: Use the Factor Formation to Solve Quadric Equation
Start forms the factors. first, you need to use the factors from x² and the constant factor. Multiply these two factors. Try using LCM.
While working with 3x²-5x+2=0, multiply the (+3) and (+2).
Try writing or separating them as (3x+/-?) (x+/-?) =0 each of these called parenthesis.
There will be errors but try to find these factors ( 3x-2) and (x-1). Because when you will multiply this term it will form 3x²-3x-2x+2=0
And affixing the middle terms you will find (-5x) as it says in our question.
Now you know how to form and break quadric equations into parenthesis.
Step 2: Set each Parenthesis Equal to Zero
Observe that each parenthesis is equal to zero. Reference :
(3x-2) (x-1) =0
So clearly the x has two values. We can solve two values easily from these two sets of equations. They are (3x-2)=0 and (x-1)=0
One will be counted as imaginary and the other real. But remember it is possible to have two real numbers if the coefficients are real numbers. Quadric equation has always two roots.
Step 3: Solve each Equation Respective to Zero
Solve them as it is. Do the simple math. Find the value of x.
For instance :
(3x-2)=0 =>3x=2 =>x=2/3 And, (x-1)=0 =>x=1
If x is greater than 0, it’s a real number and distinct. If x is less than 0 it’s an imaginary number and unequal. Also, s is equal to 0 a real number but equal. Now you have your values of x. Do check each of the values but do it separately. This was all about a how to solve a quadric equation, and how to make a way out of it.
So we see quadric equation, how to solve a quadric equation is not as hard as we think. It’s not about concrete ideas all the time. Learning from experience helps us better. So without any further delay start practicing. Because Practice makes a man perfect.
Also read: Math Tips That Helps in Your Math IB Exam