Despite the widespread misconception that quadratic has no practical applications, everything has significant uses in a range of other academic fields that are more focused on research and development.
The 4x ^ 2 – 5x – 12 = 0 equation is easily solved using quadratic equation formulas. There are two methods to solve this equation: directly and by using the Sridhar Acharya method. Despite this, given this equation, it is often better to utilize the direct approach.
Answer to 4x– 5x – 12 =0
If you go with the direct route, you will get two values of x. You will also be given two values for x. This is a methodical approach that will assist you in providing a straightforward solution to this equation.
First things first, the equation needs to be revised. Just copy the equation from your book or question paper onto your notepad.
Next, use the following format to write your equation down:
4×2-(2+3)x-12=0
Once this is done, divide the middle section of the equation and write it as follows:
4×2-2x-3x-12=0
After the two parts have been combined, write your equation as follows:
2x(2x-1)-3(x-4) = 0 4x ^ 2 – 5x – 12 = 0 Sridhar Acharya’s solution
But you’ll find that this equation was flawed because the results of your previous equations are unacceptable.
Having said that, there is another way to calculate this total: using the Sridhar Acharya technique. In order to do that, you must use the formula x = (-b ± √(b^2 – 4ac)) / 2a.
Here, we have to input the necessary values for x, a, and c from the equation and then replace them in this formula. If you keep on calculating, you’ll ultimately find the needed values.
(-b ± √(b2 – 4ac))/2a = x
Putting a = 4, B = 5, and c = 12, we can now find the values of a, b, and c in the Sridhar Acharya formula, which gives us x = (-5 ± √(52 – 4x4x12))/2×4
After solving the aforementioned equation, we get x= √217 + 5/8 or x= − √217 + 5/8.
Furthermore, after calculating the root value, we derive the Axis of Symmetry (dashed) {x}={ 0.62}.
Vertex x-Intercepts at the Roots at {x,y} = {0.62,-13.56}:
{x,y} = {-1.22, 0.00} At Root 1. {x,y} = { 2.47, 0.00} At Root 2.
As a result, after solving 4×2–5x–12 = 0, you obtain x= -1.22 and x= 2.47, and you may then calculate the values for x in this way.
Graph for 4×2-5x – 12 = 0:
Graph showing 4x ^ 2 – 5x – 12 = 0
Applications of Quadratic Equations
Despite the fact that quadratic equations don’t seem to be very useful in today’s world, they are more significant for several ancillary purposes. The following is a list of circumstances where quadratic equations are crucial:
Physics is one of the fields that makes extensive use of these equations to do computations. Quadratic equations are used to determine the equations for projectile motion and other important physics ideas.
In engineering, quadratic equations are widely employed to solve equations. These formulas could have to do with signal processing, electrical circuits, or structural analysis.
Although this may seem strange to hear, quadratic equations are utilized in the study of finance, especially when modeling complex financial systems and estimating tax investment returns.
