WGU OUM2 Task 4: Historical and Cultural
Contributions |Passed on First Attempt |Latest
Update with Complete Solution
14 October 2025
OUM2 Task 4: Historical and Cultural Contributions
A.
The quadratic formula has an extensive historical background that can be traced back to the
ancient Egyptians. Historical evidence suggests that while the Egyptians were skilled at
calculating the areas of various geometric shapes, they faced difficulties in determining the
lengths of the sides of these shapes. To overcome this challenge, approximately around 1500 BC,
Egyptian mathematicians created a table that detailed the relationship between the areas and the
side lengths of different shapes. Although this method was effective within its specific context, it
did not serve as a comprehensive solution applicable to all geometric scenarios ( Brahambhatt,
2021).
Further advancements arose from the Babylonians, who utilized their advanced numerical
system, which made addition and multiplication more efficient. By around 400 BC, the
Babylonians had developed the technique of completing the square, which allowed them to
tackle a wider range of area-related problems.
The pursuit of a more general formula for solving quadratic equations was first undertaken by
Greek philosophers such as Pythagoras and Euclid between 300 and 500 BC. Pythagoras
observed that the values of square roots are often not integers; however, he hesitated to accept
irrational proportions. In contrast, Euclid posited the potential existence of irrational square roots.
A notable advancement was made in 628 AD, when Indian mathematician Brahmagupta
introduced a solution to the quadratic equation in his treatise. Indian mathematicians at that time
employed the decimal system and the concept of zero, enabling them to engage with irrational
numbers both theoretically and practically. Brahmagupta was the first to acknowledge that
quadratic equations yield two roots.
Throughout the centuries, various versions of the quadratic equation emerged, gradually
evolving into the formula recognized today. In 1637, French mathematician René Descartes
published particular cases of the quadratic formula, using the mathematical notation and symbols
established by François Viète (Brahambhatt, 2021). Ultimately, Descartes's contributions played
a significant role in shaping the modern understanding of the quadratic formula.
B.
Having an understanding of the historical development of the quadratic formula allows for
insight that can be used to enhance the instruction and create more learning opportunities for
secondary students in algebra. It would be a great discovery opportunity for students to attempt
to solve a problem using the geometric approach taken by the Babylonians. I would start by
working one out with the students as an entire class to walk them through the process and then
have them work in groups to solve additional problems on their own. This activity could be used
for the variations of the formula as it developed over time.
Using the historical development of the quadratic formula within the lesson is also a way to
help engage students and their curiosity. Too often am I asked by my students “who created this”
or “when am I going to use this”. By going over the history of the concept, it shows the students
where the mathematical concept originally started and how much it has changed over time. The
students can see first hand how much it changed overtime and how with time it became an easier
to use formula and overall concept.
Contributions |Passed on First Attempt |Latest
Update with Complete Solution
14 October 2025
OUM2 Task 4: Historical and Cultural Contributions
A.
The quadratic formula has an extensive historical background that can be traced back to the
ancient Egyptians. Historical evidence suggests that while the Egyptians were skilled at
calculating the areas of various geometric shapes, they faced difficulties in determining the
lengths of the sides of these shapes. To overcome this challenge, approximately around 1500 BC,
Egyptian mathematicians created a table that detailed the relationship between the areas and the
side lengths of different shapes. Although this method was effective within its specific context, it
did not serve as a comprehensive solution applicable to all geometric scenarios ( Brahambhatt,
2021).
Further advancements arose from the Babylonians, who utilized their advanced numerical
system, which made addition and multiplication more efficient. By around 400 BC, the
Babylonians had developed the technique of completing the square, which allowed them to
tackle a wider range of area-related problems.
The pursuit of a more general formula for solving quadratic equations was first undertaken by
Greek philosophers such as Pythagoras and Euclid between 300 and 500 BC. Pythagoras
observed that the values of square roots are often not integers; however, he hesitated to accept
irrational proportions. In contrast, Euclid posited the potential existence of irrational square roots.
A notable advancement was made in 628 AD, when Indian mathematician Brahmagupta
introduced a solution to the quadratic equation in his treatise. Indian mathematicians at that time
employed the decimal system and the concept of zero, enabling them to engage with irrational
numbers both theoretically and practically. Brahmagupta was the first to acknowledge that
quadratic equations yield two roots.
Throughout the centuries, various versions of the quadratic equation emerged, gradually
evolving into the formula recognized today. In 1637, French mathematician René Descartes
published particular cases of the quadratic formula, using the mathematical notation and symbols
established by François Viète (Brahambhatt, 2021). Ultimately, Descartes's contributions played
a significant role in shaping the modern understanding of the quadratic formula.
B.
Having an understanding of the historical development of the quadratic formula allows for
insight that can be used to enhance the instruction and create more learning opportunities for
secondary students in algebra. It would be a great discovery opportunity for students to attempt
to solve a problem using the geometric approach taken by the Babylonians. I would start by
working one out with the students as an entire class to walk them through the process and then
have them work in groups to solve additional problems on their own. This activity could be used
for the variations of the formula as it developed over time.
Using the historical development of the quadratic formula within the lesson is also a way to
help engage students and their curiosity. Too often am I asked by my students “who created this”
or “when am I going to use this”. By going over the history of the concept, it shows the students
where the mathematical concept originally started and how much it has changed over time. The
students can see first hand how much it changed overtime and how with time it became an easier
to use formula and overall concept.
