Are you a math student, struggling to solve algebra problems? Algebra can be fun and tricky at the same time, most of the students face difficulty while dealing with polynomial expressions and derivation. Technology is very helpful to provide some online tools like differentiation calculator, iterated integral calculator, and many more. Whenever we talk about polynomial equations, a famous formula comes in our mind, known as the quadratic formula.
In this article, we will discuss this equation and quadratic formula in detail and put light on possible means to solve the equation for the value of x.
Now, let’s get started, a quadratic equation is a second degree polynomial equation, since the greatest power is a power of 2. A quadratic equation is expressed in algebra as any equation with the following form:
ax2 + bx + c = 0
It is derived from a Latin word called quadratus; means square, because the variable x has a power of 2. In the above expression, x represents an unknown term, where a, b and c are simply numbers that are known. An important thing to consider is that if a≠0, if it is equal to zero, the equation would no longer remain quadratic, and it will become linear.
The numbers a, b and c are called the quadratic coefficients. Now, the equation can be solved using factoring or by completing the square method. We will focus on completing the square method which also gives us the quadratic formula.
Completing the square method:
Consider an example, solve x2 + 4x +2 = 0
Step 1: At first, move the number term to the right side.
x2 + 4x = -2
Step 2: Now, complete the square and add the same term to the right side to balance the equation.
Here, (b/2)2 = (4/2)2 = 4, Now add this term on both sides
The equation becomes; x2 + 4x + 4 = -2 + 4
(x + 2)2 = 2
Step 3: Take square root on both sides of the equation.
Now, x + 2 = ±√2 = x + 2 = ± 1.41
Step 4: In the end, subtract 2 from both sides, x= -3.41 or -0.59
Use of Quadratic formula:
We can also use the quadratic formula for the above mentioned example. The formula is derived using the same procedure of completing the square, and is expressed as:
X = -b ±√b2 – 4ac / 2a
All you need to do is introduce the values of the three coefficients a, b and c and solve the equation for the value of x. Sometimes, it is better to go with the square completion method as in that method we are left with just one x in the end.
Use of online tool:
Well, there is one easy way out to solve these problems of equations, and that is to get assistance from an online tool. One such gizmo, available online is a quadratic formula calculator, it works on the same principle of the formula, the only difference is that it computes it quickly. This specially designed smart tool is well equipped to counter any quadratic problem.
All that is required is to feed it with the coefficient values; a, b and c. That’s it! You are all set. After understanding the concept and working on the formula, you should try an online derivative calculator.
Directional Derivative and Second Derivative are the types of differentiation. They are slightly different concepts, and their formulas are different. You can find the directional and second derivatives using an online directional derivative calculator and second derivative calculator.
In the end, all these methods work just fine and it’s up to you to select any of these techniques, depending on the time availability and interest. Good luck!
holymaths 