Reading this chapter was really interesting and I definitely would say that I learned something new, for example; I didn’t know that a muslim mathematician named this algebra, al-jabr and that it translates to restoring. Now that I got a better idea about the quadratic formula, I feel like as long as you know the standard form and you are able to remember or just recognize the quadratic formula, then this would make the formula more practical as it would be used often by mathematicians as well as students since students are taught and do learn about it at school, even though it is known but not as practical, not many people like using it and many people try to avoid using the quadratic formula.
The standard form is which makes the quadratic formula really straightforward when you memorize it because all you have to do is put in the numbers of a, b, and c to find x which serves as an unknown number unlike the others which are constants. You can put the numbers into the formula as long as you have the equation which would be equal to zero or you would have to put it in standard form to equal zero. You can solve quadratic equations in many ways, for example, using the quadratic formula or completing the square which is another way and they would both give you a positive and a negative solution, but depending on the context of the question, you might only be able to use one of the answers because you can’t always have negative numbers. As we have learned in class if the number if the square root is negative then you will have no real solution but at the time the mathematicians did not look at negative numbers as negatives had no meaning in geometry, but now positive and negatives are both used in math, and algebra even though al-khwarizmi wasn’t the one to figure out that negatives could also be solutions. If you want to check how many solutions you will have, you can find the discriminant. To find the discriminant you do which is part of the quadratic formula.
If your solution equals zero then you only have 1 solution but if the discriminant is a number greater than zero, then you will have two solutions because one positive and one is negative solution.