Question

is anyone can solve the quadratic formula or derive it?

Answer 1

I first derived this in class 8 :

ax² + bx + c = 0

= > a²x² + abx + ac = 0

= > a²x² + abx = - ac

= > a²x² + abx + b²/4  = b²/4 -  ac

= > a²x² + 2 a (b/2) x + ( b/2 )² = ( b² - 4 ac ) / 4

= > ( ax + b / 2 )² = ( b² - 4 ac ) / 4

= > ax + b / 2 = ± √ ( b² - 4 ac ) / 2

= > ax = - b/2 ± √ ( b² - 4 ac ) / 2

= > x = [  -b ± √ ( b² - 4 ac ) ] / 2 a

[ Proved ]

Thats how you solve a quadratic equation .

A quadratic equation is of form a x² + b x + c = 0

For example :

3 x² + 4 x + 1 = 0

You can also solve by factorization ..

3 x² + 4 x + 1 = 0

= >  3 x² + 3 x + x + 1 = 0

= > 3 x ( x + 1 ) + 1 ( x + 1 ) =0

= > ( 3 x + 1 )( x + 1 ) =0

= > x = -1/3 or -1

In fact I can prove in any number of methods.

Just take a random number then complete the square to get the answer .

Its easy and it allows to have fairly basic equation and algebra concepts.