Question

Derive the Quadratic Equation Formula.

{ALIGARH MUSLIM UNIVERSITY}

Answer 1

HELLO DEAR,


THE DERIVATION OF THIS FORMULA CAN BE OUTLINED AS FOLLOWS:

DIVIDE BOTH SIDES OF THE EQUATION ax2 + bx + c = 0 by a.

Transpose The Quantity c/a To The RIGHT Side OF The Equation.

Complete The Square By Adding b2 / 4a2 to Both Sides Of The Equation.

Factor The Left Side And Combine The Right Side.

EXTRACT The Square- Of Both Sides Of The Equation.

SOLVE For x By Transporting The Quantity b / 2a To The Right Side Of The Equation.

COMBINE The Right Side Of The Equation To Get The Quadratic Formula.


NOW SEE THE DERIVATION FORMULA


Derivation of Quadratic Formula

$a {x}^{2} + bx + c = 0 \\ = > {x}^{2} + \frac{bx}{a} + \frac{c}{a} = 0 \\ = > {x}^{2} + \frac{b}{x} x = - \frac{c}{a} \\ = > {x}^{2} + \frac{b}{a} x + \frac{ {b}^{2} }{4a} - \frac{ {b}^{2} }{4a } = - \frac{c}{a} \\ = > (x + \frac{b}{2a} ) ^{2} - \frac{ {b}^{2} }{4a} = - \frac{c}{a} \\ = > (x + \frac{b}{2a} x) ^{2} = \frac{ {b}^{2} }{4a} - \frac{c}{a} \\ = > (x + \frac{b}{2a} x) ^{2} = \frac{ {b}^{2} - 4ac}{4a} \\ = >( x + \frac{b}{2a}) = \frac{ + - \sqrt{ {b}^{2} - 4ac} }{2a} \\ = > x = - \frac{b}{2a} + - \frac{ \sqrt{ {b}^{2} - 4ac} }{2a} \\ = > x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac } }{2a}$


I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

HEYA!!!

The total derivation is in the image... The solution is directly done without explanation...


HOPE THIS HELPS U. @MP #MAHABOOBPASHA #☺☺