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Home » 2X^2 – 3X – 5 = 0 | Solving Quadratic Equations
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2X^2 – 3X – 5 = 0 | Solving Quadratic Equations

adarshBy adarshOctober 26, 2023Updated:October 26, 2023No Comments7 Views
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2X^2 - 3X - 5 = 0
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Quadratic equations play a fundamental role in mathematics and find application in numerous fields of research and engineering. An eXample of such a quadratic equation is “2X^2 – 3X – 5 = 0,” a familiar sight in mathematical problem-solving. This article delves deeply into the methods and strategies employed to determine the solutions of this quadratic equation. Find the roots of the quadratic equation by using the quadratic formula 2×2-3x-5=0.

Exploring the Quadratic Equation: A Brief Overview

The quadratic equation is a fundamental rule in algebra, which is represented as AX^2+bX+c=0. This equation involves the variables a,b,c,and X and it seeks to find solutions for these coefficients. In a specific example, the equation 2X^2-3X-0=0 yields the results a=2,b=-3,and c=0.

Exploring Diverse Approaches for Solving Quadratic Equations 

  1. Factoring: Revealing the Fundamental Components

Factoring is a method that involves dismantling a compleX eXpression into simpler elements, akin to disassembling a puzzle. However, in cases where the coefficients in the equation, such as 2X^2 – 3X – 5 = 0, do not easily lead to integer solutions, alternative techniques must be considered.

  1. Finding the Quadratic Formula: An Advance in Mathematic

Among the mathematical tools at our disposal, the quadratic formula stands out as a powerful instrument capable of resolving quadratic equations of various forms. The quadratic formula can be eXpressed as X = (-b ± √(b² – 4ac)) / (2a), where a, b, and c pertain to the coefficients in the equation aX² + bX + c = 0.

Applying this formula to our equation with its coefficients leads us to: X = (3 ± √((-3)^2 – 4(2)(-5))) / 2(2).

Computing the discriminant, denoted as D: D = (-3)^2 – 4(2)(-5) = 9 + 40 = 49.

This journey yields two potential solutions for X. 

  1. Navigating through the Process of Completing the Square

Completing the square presents itself as an alternative method to tackle quadratic equations. By transforming the equation into a perfect square trinomial and skillfully isolating X, this approach unveils its elegance.

  1. The Art of Graphical Analysis

Harnessing the power of graphical representation, we can gain valuable insights into the roots of quadratic equations. The points where the graph intersects the X-aXis reveal the concealed solutions, creating a visual  masterpiece of mathematical eXploration.

Unraveling the Mystery of the Quadratic Equation 2X^2 – 3X – 5 = 0: A Detailed Guide

  1. Embracing the Quadratic Formula

Let’s embark on a mathematical journey as we eXplore the quadratic equation 2X^2 – 3X – 5 = 0 using the well-established methods:

  • First, recall the quadratic formula: X = (-b ± √(b^2 – 4ac)) / 2a
  • Now, plug in the coefficients from our equation: X = (3 ± √((-3)^2 – 4(2)(-5))) / (2(2))
  • Calculating the discriminant, represented as D: D = (-3)^2 – 4(2)(-5) = 9 + 40 = 49
  • X may be solved as  X= (3+49)/4 or X=(3-49)/4.
  • X=(3+7)/4 or X=(3-7)/4 yields X=10/4 or X=-4/4, respectively, which leads in X = 2.5 or X = -1.
  1. The Graphical EXploration

To validate our solutions, let’s embark on a graphical voyage and plot the equation 2X^2 – 3X – 5 = 0. The points where the curve intersects the X-aXis materialize, closely matching X = 2.5 and X = -1, confirming our earlier calculations.

Conclusion

The quadratic equation 2X^2-3-5=0 has been effectively resolved through the using of the quadratic formula. The resulting solutions, X=2 and X=-1, denote the specific values of “X” that satisfy the equation. Quadratic equations play a pivotal role in multiple domains, and the proficiency in solving them constitutes a fundamental mathematical skill. A comprehensive grasp of the quadratic formula and its application equips individuals with the capability to tackle a diverse array of mathematical and practical challenges. 

2X^2 - 3X - 5 = 0 2x2-3x-5=0 factoring 2x2-3x-5=0 quadratic formula
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