Math is a wide subject and numerous topics come under it. The quadratic equation is one of them. To solve this equation, one needs to remember the formula and have basic mathematical knowledge to apply it. A Math equation can be solved in multiple ways, quadratic equations are mainly solved using the simplification method, we need to simplify the equation till both the sides become same i.e. L.H.S = R.H.S.
Quadratic equations contain variables and numbers, one needs to solve them. In this post, we will learn to solve quadratic equations by solving 4x ^ 2 – 5x – 12 = 0 quadratic equations.
So, keep reading this post to learn about quadratic equations and solve the 4x ^ 2 – 5x – 12 = 0 equation.
What Does Quadratic Equation Mean?
It is a problem-based equation and its name is taken from the Latin word quadratus. You need to solve this equation using a formula and follow the appropriate way of solving it to find the right answer in less time. They are represented as ax^2 + bx + c = 0.
In the given formula:
- The characters a, b, and c are known coefficients.
- X is a variable.
- A ≠ 0
For example, 4x ^ 2 – 5x – 12 = 0, is a quadratic equation. Its type is a polynomial equation.
Now, you may wonder why a ≠ 0 in the above formula. So, let’s understand it.
Reason Behind “Why Coefficient ‘A’ ≠ 0 In The Quadratic Equation?”
In school, you must have learned or read that A ≠ 0 in a quadratic equation. It is because of contradictory rules, that every math equation has its rules. If we consider the value of the coefficient A = 0, the equation will become a linear equation and the concept of quadratic equation will change.
Quadratic Formula To Solve Equation 4x ^ 2 – 5x – 12 = 0
The equation 4x ^ 2 – 5x – 12 = 0 can be solved by using the formula x = [ -b ± √ (b2 – 4ac)] / 2a. After applying the formula, you need to put the question’s figures in it and keep simplifying the calculator to find the answer.
This formula is widely used to solve quadratic equations.
How To Solve The Equation 4x ^ 2 – 5x – 12 = 0?
The equation to solve is 4x ^ 2 – 5x – 12 = 0.
The Quadratic formula to apply: x = [ -b ± √ (b2 – 4ac)] / 2a
As we have already discussed, a, b, and c, are the coefficient. In this question, values are a = 4, b = -5, and c = -12. X is a variable and its value is not given in the equation, so we will take its value x i.e. X = x.
Now, put all values in the formula.
x = [ -b ± √ (b2 – 4ac)] / 2a,
x = [ – (-5) ± √ ( (-5)2– 4 (4) (-12))] / 2 (4)
x = [ 5 ± √ ( 25 +192 )] / 8
x = [5 ± √ ( 217 )] / 8
x = 5 + √ 217 / 8 and x = 5 – √ 217 / 8
So, x = 2.466 and x = – 1.216
The two solutions of the equations are x = 2.466 and x = – 1. The former one comes when we take positive value and the second one comes when we take the negative value.
Conclusion
Math is a subject that requires practice and the right understanding of the subject to solve any question. If you achieve these two things, you can solve any question, whether complex or easy.
Many students fear quadratic equations, they are not hard but require practice and experience in applying the formula in the manner to get the answer. We hope that this post helped you understand the concept of quadratic equations. Now, remember the formula x = [ -b ± √ (b2 – 4ac)] / 2a and solve some more questions like 4x ^ 2 – 5x – 12 = 0 to perfect your concept. Share this post about quadratic equations with other students as well to help them in their studies.
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