Quadratic equation isn’t an unknown thing for math lovers. However, there are so many people who still struggle while solving 4x ^ 2 – 5x – 12 = 0. Well, it’s not that hard to solve an algebra equation. You have to try out some easy methods.
You might know that quadratic equations are very essential in algebra. Plus, there are so many applications in the real world. After doing some research, we found the easiest ways to solve this equation.
In this guide, we will share these equations. Moreover, we will also cover the characteristics, real-world applications, and more. So, let’s get started.
What is the Quadratic Equation?
Before we start with the best methods, you need to understand the basics of the quadratic equation. As we noted before, this is a crucial equation in algebra. These are polynomial equations or second degree.
Well, this means these equations involve variables raised with the power of two. To understand this equation, let’s break down a formula. For example, in this ax^2 + bx + c = 0 equation, ‘x’ is variable. On the other hand, the constants are ‘a’, ‘b’, and ‘c’. In this case, we have to use ‘x’ for solving the method.
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Characteristics of Quadratic Equation
By reading this article, you can understand that the quadratic equation is essential for study and solution. It’s essential to understand the characteristics that help us gain knowledge about practical and real-world applications. However, you need to try out the easiest method for a better understanding.
How to Solve Quadratic Equation 4x ^ 2 – 5x – 12 = 0
Now, you know the basics of quadratic equations. If you are ready to solve them, we found some easiest methods. It will be quite interesting as well. Keep reading the following section to know more about these equations:
Factoring Method
Factoring method is one of the easiest methods. In this case, you have to break down the equations into two factors. And these two factors can be solved individually. However, you can only use this method when the equation is factorable. Let’s find out how to do this:
To solve 4x^2 – 5x – 12 = 0, we have to find two binomials at first. Well, these binomials have to multiply together for the quadratic equations. In this case, the form will be (2x + 3)(2x – 4) = 0.
When we equate two factors, there will be two equations; 2x – 4 = 0 and 2x + 3 = 0. So, the factoring method gives the value of ‘x’. So, the value of ‘x’ can be x= 2 and x= -3/2.
Quadratic Formula
If you want to try out another simple method, the quadratic formula is the best one. In fact, most people prefer this method over others. The best part is it’s a powerful tool that gives a guaranteed solution.
For solving 4x^2 – 5x – 12 = 0, we have to use the formula of x = (-b ± √(b^2 – 4ac)) / 2a. Now, you have to plug in the values of a=4, b= -5, and c= -12. As we break down the formula, we can find the value of ‘x’. By doing this, we can find the solution x= -3/2 and x= 2.
Real World Quadratic Equation Applications
Sure, we have solved different quadratic equations in algebra. But, what’s the use in the real world? If this question is bugging you, we have the best answer. Of course, quadratic equations are very useful in the real world. Keep reading the following section as we discover the real-world applications:
Projectile Motion: A quadratic equation plays a crucial role in understanding the motion of a projectile. Whether a rocket is being launched or a bullet is being fired, the path can be modeled using a quadratic equation. To predict the object’s trajectory, we can consider the angle of projection and initial velocity.
Engineering and Design: You might know that quadratic equations are used in various fields. However, these equations are very useful for designing and engineering. For example, some real world applications are designing bridges and determining optimal shapes for designing structures. On the other hand, these can be used for understanding how materials are going to perform under stress.
Optics: Another essential real world application is for the optic materials. It’s essential to use quadratic equations for designing lenses and mirrors. That’s why these formulas are quite popular for making cameras. On the other hand, it can be used for making telescopes as well.
Finance: Not just the engineering and optics world, you can also use these formulas for theoretical sectors. For example, these equations are very useful for the finance and economics sectors. They can be helpful for optimum production levels and maximizing profits. However, these equations are not necessary for the finance world all the time.
These are the common applications for these equations. However, some other sectors also implement them in some cases. In short, they are very useful for some sectors.
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Conclusion
Finally, you have the idea of solving 4x ^ 2 – 5x – 12 = 0. We shared different methods in this article to solve the problem. Now, it depends on you; here you can use either quadratic formula or factoring method as per your preference. Before that, you have to understand the quadratic equation. If you want to know more, search more on the internet.
FAQs
Q: What are 4 examples of quadratic equations?
There are four examples of quadratic equations including 2x² – 64 = 0, x² – 16 = 0, 6x² + 11x – 35 = 0, x² – 7x = 0, 2x² + 8x = 0, and 2x² – 4x – 2 = 0.
Q: How to solve quadratic?
If you want to solve quadratic equations, you can either try out the factoring method or the quadratic formula. Well, if you want an accurate result, you have to try out the second one.
Q: What are the real world quadratic equation applications?
There are some excellent real-world applications for these equations including engineering, designing, projectile motion, optics, finance, economics, and more.