SOLUTION: Can someone please help me with this problem? I am stumped! This is the problem: Show how the quadratic formula can be expressed as: {{{-p/2}}}±{{{ sqrt( p^2/4-q ) }}}

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Can someone please help me with this problem? I am stumped! This is the problem: Show how the quadratic formula can be expressed as: {{{-p/2}}}±{{{ sqrt( p^2/4-q ) }}}       Log On


   

Question 25681: Can someone please help me with this problem? I am stumped! This is the problem:
Show how the quadratic formula can be expressed as:
-p%2F2±+sqrt%28+p%5E2%2F4-q+%29+

let p=b%2Fa and q=c%2Fa
It says that it can be derived by "completing" the square of a quadratic equation. A response to this problem would really make my day!
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
-p%2F2±+sqrt%28+p%5E2%2F4-q+%29+

let p=b%2Fa and q=c%2Fa
It says that it can be derived by "completing" the square of a quadratic equation. A response to this problem would really make my day!
-------------------------------------------------------------------------------
SUBSTITUTE IN THE ANSWER GIVEN BELOW YOUR NOMENCLATURE THAT
p=b%2Fa and q=c%2Fa..AND YOU WILL GET YOUR ANSWER
LET THE QUADRATIC BE
AX^2+BX+C=0...SINCE THIS IS A QUADRATIC ,A IS NOT EQUAL TO ZERO..SO DIVIDING WITH A WE GET
X^2+BX/A+C/A=0
WRITE IT AS A PERFECT SQUARE USING X^2 AND X TERMS
{X^2+2*X*(B/2A)+(B/2A)^2}-(B/2A)^2+C/A=0
{X+(B/2A)}^2=(B/2A)^2-C/A=B^2/4A^2-C/A=(B^2-4AC)/4A^2
TAKING SQUARE ROOT
X+B/2A=%28PLUS+OR+MINUS+sqrt%28+B%5E2-4%2AA%2AC+%29%29%2F%282%2AA%29+
OR
x+=+%28-B+%2B-+sqrt%28+B%5E2-4%2AA%2AC+%29%29%2F%282%2AA%29+
THIS IS THE GENERAL METHOD OF DERIVATION OF ROOTS OF A QUADRATIC EQUATION.