Question

Hello friends ... this is a tutorial that contains some interesting facts about quadratic equations ...

Answer 1

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

Answer 2

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 :
\[\large{\alpha*\beta=(\frac{-b+\sqrt{b^2-4ac}}{2a})*(\frac{-b-\sqrt{b^2-4ac}}{2a})}\]
\[\large{\alpha*\beta=\frac{b^2-b^2+4ac}{4a^2}}\]
\[\large{\alpha*\beta=\frac{4ac}{4a^2}}\]
\[\huge{\alpha*\beta=\frac{c}{a}}\]

Answer 3

very nice @mathslover

Answer 4

thanks @lalaly

Answer 5

gr8:)

Answer 6

thanks @maheshmeghwal9

Answer 7

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

Answer 8

It is Vieta's formulas for the quadratic equation.

Answer 9

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

Answer 10

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