Solve Quadratic equations: 4x ^ 2 – 5x – 12 = 0

4x ^ 2 – 5x – 12 = 0 is an example of a quadratic equation. This equation is a mathematical equation and it requires a formula to solve it. This is one of the mathematical equation-based questions where variables and numbers are given. In this equation, we have to simply prove that left hand side is equal to right hand side (L.H.S = R.H.S).

4x ^ 2 – 5x – 12 = 0, is one of the quadratic equation forms. This type of quadratic equations problem generally solved by simplification method. This method involves breaking of equations till it equalizes the equation. Mathematical equations a just seemed to be complex but they’re actually difficult. It requires basic mathematical knowledge and formulas to solve any equations.

About Quadratic Equation 4x ^ 2 – 5x – 12 = 0

Quadratic equation is a mathematical term. Quadratic Equation a problem-based equation that is asked to solve to prove a solution. It is derived from a Latin word quadratus. 4x ^ 2 – 5x – 12 = 0, is a prime example of quadratic equation. A polynomial equation of a second degree where atleast one of the variables have a square on it.  Quadratic equations are represented in the form of ax^2 + bx + c = 0.

Example:

  • In the given equation, ax^2 + bx + c = 0
  • a, b, c are called as a known coefficient where a is not equal 0
  • x is represented as variable.

Why coefficient ‘a’ is not equal to zero in a quadratic equation?

We all have learned that Coefficient ‘a’ can never be represented with a value 0. Mathematics have rules and regulations for each mathematical concept. Quadratic equation will get converted to a linear equation if coefficient ‘a’ is represented equal to 0 which means it will alter the whole equation.

Formula to solve 4x ^ 2 – 5x – 12 = 0

Given term is an example of quadratic equation, and it requires a special formula to solve such kinds of problems in mathematics.

Quadratic Formula: x = [ -b   (b2 – 4ac)] / 2a

This is an accurate and verified formula to solve quadratic equations and related problems. This formula is a formula of simplification in which we simplify the equation as much as possible. This technique is a best method to solve the equation, 4x ^ 2 – 5x – 12 = 0.

Four different Methods to Solve 4x ^ 2 – 5x – 12 = 0

Factoring is a technique to solve an equation by splitting the middle terms of the equation. Factoring technique is used to determine the factors of an equation and then it is solved.

Using Quadratic Formula

x = [ -b   (b2 – 4ac)] / 2a, this is a quadratic formula, by simply adding all the respective values in this formula we can find a right solution.

Taking the Square Root

Taking the square root is a method to find a solution for solving Quadratic Equation. In this technique we solve the roots of both the sides to get an accurate answer for this. This method applicable only when the squared variable is brought to the one side and the constant terms shifted to other side.

Completing the square

Divide the equation by the coefficient of square variable. It means divide the equation by the coefficient ‘a’ then imply the square method. Add a constant term on both the sides of the equation and calculate.

Solution of the 4x ^ 2 – 5x – 12 = 0

  • We will solve the equation by quadratic formula.
  • Quadratic formula: x = [ -b ± √ (b2 – 4ac)] / 2a
  • In this given equation: a = 4, b = – 5 and c  = – 12 where a is not equal to 0.
  • X is an unknown factor or a variable.
  • Put all the respective values in the quadratic formula.

Assume, X = x

  • Quadratic 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

Thus, x = 2.466 and x = – 1.216

Two consecutive solution for the equation are: x = 2.466 and x = – 1

Some examples of quadratic equations:

  • x2 – 2x – 24 = 0
  • 2x2 + 4x – 5 = 0
  • x2 – 1x – 6 = 0

These are three examples of what quadratic equations looks like. These equations are further solved with the help of quadratic formula to find the value of ‘x’.

Conclusion

4x ^ 2 – 5x – 12 = 0, is an example of quadratic equation. This equation can be solve by four different methods. In this equation we have to find the value of the x, by breaking down the equation as per the mathematical order. Quadratic equations is a small universe in the cosmos of mathematics.

Quadratic equations are very easy to solve when we apply the right formula. If we have the formula, we have just put the right value at the right position and it’s done. 4x ^ 2 – 5x – 12 = 0 an equation and it can asked in the format of multiple choice questions also.

For any quadratic equations same quadratic formula is used to find the value of ‘x’. Mathematics just looks difficult but it’s not a difficult subject. Mathematics is a game of formula, if you know the formula you can crack all the mathematical problems.

FAQs

  1. What is Quadratic Equation?

Quadratic equation is a mathematical term. Quadratic Equation a problem-based equation that asked to be solve to prove a solution. It iderived from a Latin word quadratus.

  1. What is the solution for 4x ^ 2 – 5x – 12 = 0.

As per the quadratic formula there are two solutions for it. The two consecutive solution for the equation are: x = 2.466 and x = – 1. We generally avoid the negative one for further calculations.

  1. What is the formula of quadratic equation?

Quadratic formula: x = [ -b ± √ (b2 – 4ac)] / 2a. In this given equation: a = 4, b = – 5 and c  = – 12 where a is not equal to 0.

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