I’m can’t freakin stay up I need to sleep and I need to get 4 papers done for my portfolio I can’t help but I wish you luck
Step-by-step explanation:
everything can be found in the picture
Answer:
![\alpha + \beta = -\frac{b}{a}](https://tex.z-dn.net/?f=%5Calpha%20%2B%20%5Cbeta%20%3D%20-%5Cfrac%7Bb%7D%7Ba%7D)
![\alpha \beta = \frac{c}{a}](https://tex.z-dn.net/?f=%5Calpha%20%20%5Cbeta%20%3D%20%5Cfrac%7Bc%7D%7Ba%7D)
Step-by-step explanation:
Given
![ax^2 + bx + c = 0](https://tex.z-dn.net/?f=ax%5E2%20%2B%20bx%20%2B%20c%20%3D%200)
![Roots: \alpha \& \beta](https://tex.z-dn.net/?f=Roots%3A%20%5Calpha%20%5C%26%20%5Cbeta)
Required
Show that:
![\alpha + \beta = -\frac{b}{a}](https://tex.z-dn.net/?f=%5Calpha%20%2B%20%5Cbeta%20%3D%20-%5Cfrac%7Bb%7D%7Ba%7D)
![\alpha \beta = \frac{c}{a}](https://tex.z-dn.net/?f=%5Calpha%20%5Cbeta%20%3D%20%5Cfrac%7Bc%7D%7Ba%7D)
![ax^2 + bx + c = 0](https://tex.z-dn.net/?f=ax%5E2%20%2B%20bx%20%2B%20c%20%3D%200)
Divide through by a
![\frac{a}{a}x^2 + \frac{b}{a}x + \frac{c}{a} = \frac{0}{a}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7Ba%7Dx%5E2%20%2B%20%5Cfrac%7Bb%7D%7Ba%7Dx%20%2B%20%5Cfrac%7Bc%7D%7Ba%7D%20%3D%20%5Cfrac%7B0%7D%7Ba%7D)
![x^2 + \frac{b}{a}x + \frac{c}{a} = 0](https://tex.z-dn.net/?f=x%5E2%20%2B%20%5Cfrac%7Bb%7D%7Ba%7Dx%20%2B%20%5Cfrac%7Bc%7D%7Ba%7D%20%3D%200)
The general form of a quadratic equation is:
![x^2 - (Sum)x + (Product) = 0](https://tex.z-dn.net/?f=x%5E2%20-%20%28Sum%29x%20%2B%20%28Product%29%20%3D%200)
By comparison, we have:
![-(Sum)x = \frac{b}{a}x](https://tex.z-dn.net/?f=-%28Sum%29x%20%3D%20%5Cfrac%7Bb%7D%7Ba%7Dx)
![-(Sum) = \frac{b}{a}](https://tex.z-dn.net/?f=-%28Sum%29%20%3D%20%5Cfrac%7Bb%7D%7Ba%7D)
Sum is calculated as:
![Sum = \alpha + \beta](https://tex.z-dn.net/?f=Sum%20%3D%20%5Calpha%20%2B%20%5Cbeta)
So, we have:
![-(\alpha + \beta) = \frac{b}{a}](https://tex.z-dn.net/?f=-%28%5Calpha%20%2B%20%5Cbeta%29%20%3D%20%5Cfrac%7Bb%7D%7Ba%7D)
Divide both sides by -1
![\alpha + \beta = -\frac{b}{a}](https://tex.z-dn.net/?f=%5Calpha%20%2B%20%5Cbeta%20%3D%20-%5Cfrac%7Bb%7D%7Ba%7D)
Similarly;
![Product = \frac{c}{a}](https://tex.z-dn.net/?f=Product%20%3D%20%5Cfrac%7Bc%7D%7Ba%7D)
Product is calculated as:
![Product = \alpha * \beta](https://tex.z-dn.net/?f=Product%20%3D%20%5Calpha%20%2A%20%5Cbeta)
So, we have:
![\alpha * \beta = \frac{c}{a}](https://tex.z-dn.net/?f=%5Calpha%20%2A%20%5Cbeta%20%3D%20%5Cfrac%7Bc%7D%7Ba%7D)
![\alpha \beta = \frac{c}{a}](https://tex.z-dn.net/?f=%5Calpha%20%20%5Cbeta%20%3D%20%5Cfrac%7Bc%7D%7Ba%7D)
Answer:
2 hours and 27 minutes
Step-by-step explanation:
300 divided by 132.1 = 2.271
2.27 (simplified)
No,It Won't. Because It Increases Right, Do You Get It?