Question

Hey guys......

Plz derive the quadratic formula......

Answer 1

Hi buddy ☺

 

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-root 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.

See the derivation below.
 

Derivation of Quadratic Formula
ax2+bx+c=0ax2+bx+c=0

x2+bax+ca=0x2+bax+ca=0

x2+bax=−cax2+bax=−ca

x2+bax+b24a2=b24a2−cax2+bax+b24a2=b24a2−ca

(x+b2a)2=b2−4ac4a2(x+b2a)2=b2−4ac4a2

. x+b2a=±b2−4ac−−−−−−−√2ax+b2a=±b2−4ac2a

x=−b2a±b2−4ac−−−−−−−√2ax=−b2a±b2−4ac2a

x=−b±b2−4ac−−−−−−−√2a

Answer 2

General formula
$a {x }^{2} + bx + c$
Hope it helps you