The factored form of the given quadratic equation is [tex](2x-5)(2x+5)[/tex]
Definition of Quadratic Equation
- A quadratic equation is an algebraic equation with highest power 2.
- It is expressed in the standard form as [tex]ax^{2} + bx + c[/tex], where a, b, and c are constants and [tex]x[/tex] is a variable with degree 2.
Derivation of factored form of given equation:
Given,
A quadratic equation [tex]4x^{2} - 20x + 25[/tex]
Using middle term splitting method to factorize the equation, we need to split the middle term of the equation in such a way that the terms used when multiplied together give [tex]100x^{2}[/tex] [tex](25*4x^{2} )[/tex] as result and when added, give [tex]-20x[/tex] (middle term) as result.
The required terms will be [tex]-10x[/tex] and [tex]-10x[/tex]
⇒ [tex]4x^{2} -10x -10x + 25[/tex]
- Forming pair of two terms
⇒ [tex](4x^{2} -10x) - (10x -25)[/tex]
- Taking [tex]2x[/tex] and 5 common from first and second pair respectively
⇒ [tex]2x(2x-5) -5(2x-5)[/tex]
- Taking [tex](2x-5)[/tex] common
⇒ [tex](2x-5)(2x-5)[/tex]
Hence, the factored form of the given equation is [tex](2x-5)(2x-5)[/tex]
To learn more about quadratic equations, refer: https://brainly.com/question/12402430
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