For this, I understand when Greg says that the inequality is the cutline.
But what happens when the equality sign is flipped? so if its x^2 + 3x > 7
or if its not a equal or greater/ equal or less sign?
Do I still solve it like a normal quadratic like x^2 + 3x - 7 = 0 like Greg did in this video?
Also Greg mentions that there is an equation for the getting the sum of two solutions before he started using the quadratic formula. Does anyone know what equation he was referring to?
Then you’re asking the question “what region is x^2 + 3x -7 [whatever inequality sign u want ] 0 — by way of graphing or algebraically. Anyway, it’s best for you to look up how to solve quadratic inequalities in general.
Vieta’s formula.
Also, you don’t have to treat it like a “formula” because it’s very easy to see yourself (at least for now he quadratic and cubic case).
Consider the quadratic case for now (cuz that’s your actual question.
We equate two ways of expressing a quadratic equation as follows:
a(x - r_1)(x - r_2) = ax^2 + bx + c
Expand the left hand side and equate coefficients then you’ll get your “sum and product of roots formula”.
Have u tried this? If you actually work through “deriving” it then it’ll be committed to memory better.
Anyway the sum of roots of a quadratic equation is just - \frac ba, where b and a are the coefficients of a general quadratic equation (ax^2 + bx + c).
