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 process al-jabr and that it translates to restoring.
Now to my understanding of these formulas, in my opinion as long as you know the standard form and can remember the quadratic formula, then the formula would be used more often by mathematicians as well as students since students are taught and do learn about it at school, then it is known but not as practical if you don’t know it by heart. The standard form is which makes the quadratic formula really simple when you know it because all you have to do is put in the numbers of a, b, and c to find x which represents 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 one positive and one 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 you get a number greater than zero, that means you have