Question

Derive the quadratic formula from the standard quadratic equation

Answer 1

See the attached file

Answer 2

Hi ,

Let ax² + bx + c = 0 is a quadratic equation , a ≠ 0

Divide each term with 'a ' , we get

x² + bx/a + c/a = 0

x² + bx/a = - c/a

x² + 2 × x × ( b / 2a ) = - c/a

x² + 2 × x × ( b/2a ) + ( b/2a )² = - c/a+ ( b/2a )²

( x + b/2a )² = - c/a + b²/4a²

= ( -4ac + b² ) / 4a²

( x + b/2a ) = ± √( b² - 4ac ) / 2a

x = [ - b/2a ± √( b² - 4ac ) / 2a ]

= [ -b ± √( b² - 4ac ) ]/2a

I hope this helps you.

:)