by Quadratic equations are fundamental in algebra and have a wide range of applications in various fields. One such equation,x2-11x+28=0, might seem complex at first glance, but with the right approach, it can be solved efficiently. In this article, we’ll delve into the step-by-step process of solving this equation.
Before diving into the solution, it’s essential to understand the structure of a quadratic equation. A quadratic equation is of the form ax^2 + bx + c = 0, where a, b, and c are constants, and ‘a’ is not equal to zero. The solutions to this equation are often referred to as the roots or x-intercepts.
Factorization Method
One of the most common methods to solve a quadratic equation is the factorization method. Let’s apply this method to our equation, x2-11x+28=0
- Identifying the Middle Term: The middle term in our equation is -11x. We need to split this term to factorize the equation.
- Factorization: On factorizing, we get: (x^2-4x) – (7x-28) = 0 x(x-4) – 7(x-4) = 0 (x-4)(x-7) = 0
From the above factorization, we can deduce the roots of the equation: x = 4 and x = 7
Verification
To ensure the accuracy of our solution, we can substitute the roots back into the original equation:
For x=4: 4^2 – 11(4) + 28 = 0 For x=7: 7^2 – 11(7) + 28 = 0
Both equations hold true, verifying the correctness of our roots.
Conclusion
Quadratic equations might seem daunting initially, but with a systematic approach, they can be solved with ease. The equation x^2-11x+28=0 has roots 4 and 7, as derived using the factorization method. Understanding the underlying concepts and practicing regularly can make solving such equations a breeze.
