Well ! tackling real-life equations is much easier than solving quadratic equations. Many people are stuck in the way of getting a solution for it. Some of them quit just by looking at the question.
While some attempt with no hope of solving it in one go. We, here are explaining some tricks and formulas which will help you.
4x ^ 2 – 5x – 12 = 0 is a quadratic equation. This is a mathematical equation and it requires some tricks and formulas to solve it. This is an equation-based question that includes both variables and numbers.
Most of the students find difficulty in solving this. Rather than wasting your time in looking for solutions, who left you with more confusion? This post has explained the solution in a step-by-step method.
It is simple, easy, and time-saving. All you have to do is hold a book and pen and start solving together to find an accurate answer. So, let’s start
What is Quadratic Equation 4x ^ 2 – 5x – 12 = 0 Mean?
Quadratic equation is a mathematical term. This quadratic equation is called a problem-based equation that is asked to solve in case of proving a solution.
It is extracted from the Latin word quadratus. 4x ^ 2 – 5x – 12 = 0, is the prime number. It is a polynomial equation of a second degree where you can find square of at least one variable.
Usually, quadratic equations are represented in the form of ax ^ 2 + bx + c = 0
Illustration :
- In the above given equation, ax ^ 2 + bx + c = 0
- a,b,c are known as coefficients on the other side where a is not equal to 0
- X is represented as a variable.
Reasons Why Coefficient ‘a’ is not Identical to zero in a quadratic equation?
As we have understood, the coefficient ‘a’ will never be represented with a value 0. There is a bundle of rules and regulations in the concept of mathematics.
Quadratic equations will directly switch to a linear equation when coefficient ‘a’ is represented identical to 0, which means it will change the whole equation.
Formula to solve 4x ^ 2 – 5x – 12 = 0
This is an illustration of a quadratic equation, and some special formulas are needed to solve such kind of equations in mathematics.
Quadratic Formula: x = [ -b (b2 – 4ac)] / 2a
This is a precise and confirmed formula to solve quadratic equations and this kind of issue. This is a formula of simplification in which we have to simplify equations as much as we can.
This technique is a verified way to solve the equation, 4x ^ 2 – 5x – 12 = 0.
Four Ways You Can Solve 4x ^ 2 – 5x – 12 = 0
The best way to solve these types of questions is the technique of factorization, By splitting the middle of the equation.
The technique of factoring is used to determine the factor of an equation and by that, it is solved.
Using Quadratic Formula
x = [ -b (b2 – 4ac)] / 2a, this is a quadratic formula, just add all the respective values in this formula and you’ll be able to find an exact solution.
Taking square root
To find a solution for a quadratic equation the method of square root is applicable. In this, you have to solve the roots of both the ends to get an exact answer of the equation.
This process is only applicable when the squared variable is taken to one side and the constant term is moved to the other side.
Finalizing the square
Dividing the equation by the square variable’s coefficient. It indicate dividing the equation by the coefficient ‘a’ then implify the square method. Put a constant term on both the ends of the equation and calculate.
Solution ; 4x ^ 2 – 5x – 12 = 0
This equation will be solved by the quadratic formula method.
Quadratic formula: x = [ -b ± √ (b2 – 4ac)] / 2a
In the following equation: a = 4, b = – 5, and c = – 12 where a and 0 are not equal.
X is called an unknown variable.
Add all the values in the quadratic equation.
Suppose, X = x
Step-1 Quadratic formula = x= [ -b ± √ (b2 – 4ac)] / 2a
Step-2 x = [ – (-5) ± √ ( (-5)2– 4 (4) (-12))] / 2 (4)
Step-3 x = [ 5 ± √ ( 25 +192 )] / 8
Step-4 x = [ 5 ± √ ( 25 +192 )] / 8
Step-5 x = [5 ± √ ( 217 )] / 8
Step-6 5 + √ 217 / 8 and X = 5 – √ 217 / 8
Therefore, x = 2.466 and x = – 1.216
Two succeeding solutions for the equation are: x = 2.466 and x = – 1
Few illustrations of quadratic equations:
- x2 – 2x – 24 = 0
- 2×2 + 4x – 5 = 0
- x2 – 1x – 6 = 0
These are few illustrations of what a quadratic equation seems like. These equations are tallied later with the help of quadratic formulas to know the value of ‘x’
The Closure
The above quadratic equation can be solved in four different ways. In this, we have to find the value of ‘x’ by dividing the equation following mathematical terms.
Quadratic equations are not tough the way they look. We just have to place the right formula and the rest is very simple. For solving such kinds of equations you have to memorize formulas.
There is only hype created about the mathematics subject, it is not that horrifying how it looks like. Once you understand the terms and formulas of it then it is just a game of digits and variables.
You don’t have to worry about such quadratic questions, just read the question calmly and start solving it you will definitely find an accurate answer.
