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mathslover
Hello friends ... this is a tutorial that contains some interesting facts about quadratic equations ...
before viewing this view : http://openstudy.com/study#/updates/4fe08815e4b06e92b86fa074
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 : \[\large{\alpha*\beta=(\frac{-b+\sqrt{b^2-4ac}}{2a})*(\frac{-b-\sqrt{b^2-4ac}}{2a})}\] \[\large{\alpha*\beta=\frac{b^2-b^2+4ac}{4a^2}}\] \[\large{\alpha*\beta=\frac{4ac}{4a^2}}\] \[\huge{\alpha*\beta=\frac{c}{a}}\]
thanks @maheshmeghwal9
To practice problems about product and sum of roots, do some problems on http://www.saab.org/mathdrills/act.html
It is Vieta's formulas for the quadratic equation.
i wanna ask can u give me the proof of quadratic equation @mathslover ???
Why not @jiteshmeghwal9 So here i go : http://openstudy.com/study#/updates/4fe08815e4b06e92b86fa074