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4x ^ 2 – 5x – 12 = 0 and Its Roots: A Closer Look at the Solution

Hi Readers! Have you tried to solve any quadratic equation smartly? This blog will guide you to take a closer look at the solutions of one such quadratic equation. A quadratic equation like 4x ^ 2 – 5x – 12 = 0 is sometimes hard to find its solutions? Don’t worry, you’re not alone. This blog will unlock the process of solving this equation and get deeper into understanding its roots.

Quadratic equations play a vital role in various mathematical and scientific fields. They have wide-ranging applications in real-life scenarios, including physics, engineering, and computer modeling. Understanding how to solve and analyze these equations is fundamental for anyone pursuing a deeper understanding of mathematics.

What is the Meaning of This Quadratic Equation?

The given quadratic equation,4x² – 5x – 12 = 0, represents a second-degree polynomial equation where the highest power of the variable is 2. The equation includes three terms, namely the quadratic term (4x²), the linear term (-5x), and the constant term (-12).

How Can We Find the Roots of This Equation?

To find the roots (or solutions) of this quadratic equation, 4x ^ 2 – 5x – 12 = 0, we can apply the widely-used quadratic formula:
x = (-b ± √(b² – 4ac)) / (2a)
In this formula, a, b, and c represent the coefficients of the quadratic equation. For our given equation, the coefficients are as follows:
a = 4, b = -5, and c = -12.
By substituting these values into the quadratic formula, we can calculate the roots of the equation.

Analyzing the Roots

Root 1: What is the value of x for the positive root?

Using the quadratic formula, we can calculate the value of x for the positive root:
x = (-(-5) + √((-5)² – 4 * 4 * -12)) / (2 * 4)
Simplifying further, we have:
x = (5 + √(25 + 192)) / 8
x = (5 + √217) / 8
Therefore, the positive root of the equation 4x ^ 2 – 5x – 12 = 0 is (5 + √217) / 8.

Root 2: What is the value of x for the negative root?

Similarly, we can calculate the value of x for the negative root:
x = (-(-5) – √((-5)² – 4 * 4 * -12)) / (2 * 4)
Simplifying further, we have:
x = (5 – √(25 + 192)) / 8
x = (5 – √217) / 8
Therefore, the negative root of the equation 4x ^ 2 – 5x – 12 = 0 is (5 – √217) / 8.

Summary

In conclusion, by understanding the process of unlocking the solution to the quadratic equation 4x ^ 2 – 5x – 12 = 0, we can find its roots. The positive root is (5 + √217) / 8, while the negative root is (5 – √217) / 8. Solving quadratic equations not only enhances our mathematical abilities but also equips us with problem-solving skills applicable in various fields. So, the next time you encounter a quadratic equation, don’t be intimidated. Embrace the challenge and unlock its solution!

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David Scott
David Scott
Digital Marketing Specialist .
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