## mathslover 3 years ago Hello friends ... this is a tutorial that contains some interesting facts about quadratic equations ...

1. mathslover

before viewing this view : http://openstudy.com/study#/updates/4fe08815e4b06e92b86fa074

2. mathslover

HERE WE GO : Let alpha and beta are the 2 roots of the quadratic equation $$\large{ax^2+bx+c=0}$$ as per the tutorial that i posted earlier : $\huge{\alpha = \frac{-b+\sqrt{b^2-4ac}}{2a}}$ $\huge{\beta=\frac{-b-\sqrt{b^2-4ac}}{2a}}$ 1) Sum of the roots : ${\alpha + \beta = \frac{-b+\sqrt{b^2-4ac}}{2a}+\frac{-b-\sqrt{b^2-4ac}}{2a}}$ $\huge{\alpha+\beta=\frac{-2b}{2a}}$ $\huge{\alpha+\beta=\frac{-b}{a}}$ 2) Product of roots : $\large{\alpha*\beta=(\frac{-b+\sqrt{b^2-4ac}}{2a})*(\frac{-b-\sqrt{b^2-4ac}}{2a})}$ $\large{\alpha*\beta=\frac{b^2-b^2+4ac}{4a^2}}$ $\large{\alpha*\beta=\frac{4ac}{4a^2}}$ $\huge{\alpha*\beta=\frac{c}{a}}$

3. mathslover

4. lalaly

very nice @mathslover

5. mathslover

thanks @lalaly

6. maheshmeghwal9

gr8:)

7. mathslover

thanks @maheshmeghwal9

8. eliassaab

To practice problems about product and sum of roots, do some problems on http://www.saab.org/mathdrills/act.html

9. klimenkov

It is Vieta's formulas for the quadratic equation.

10. jiteshmeghwal9

i wanna ask can u give me the proof of quadratic equation @mathslover ???

11. mathslover

Why not @jiteshmeghwal9 So here i go : http://openstudy.com/study#/updates/4fe08815e4b06e92b86fa074