SOLUTION: Hi, I am really having a hard time analyzing this one, I hope someone could help me on this and I would really really appreciate it so much. Question 1 : Explain a sequence of s

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Question 23670: Hi, I am really having a hard time analyzing this one, I hope someone could help me on this and I would really really appreciate it so much.
Question 1 : Explain a sequence of steps that can be used to solve any quadratic equation in the QUICKEST WAY.
Question 2 : Derive the quadratic formula used in solving quadratic equations.
Found 2 solutions by Earlsdon, venugopalramana:
Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website!
1) Determine whether or not the quadratic equation is factorable.
If it is factorable, then factor it and apply the zero product principle to find the roots.
If it is not factorable, or you are unable to determine its factorability, then use the quadratic formula to find the roots.
2) Derive the quadratic formula:
Start with the standard form of the general quadratic equation:
Divide through by a to get the x^2 coefficient = 1.
Subtract c/a form both sides of the equation.
Complete the square in the x-terms by adding the square of half the x-coefficient to both sides.
Factor the left side.
Take the square root of both sides.
Note: There is (or should be) a + or - in front of the sqrt sign. Simplify the contents of the radical.
Take the square root of the denominator on the right side.
Subtract b/2a from both sides.
Simplify the right side.
And there you have it!

Answer by venugopalramana(3286) (Show Source):
You can put this solution on YOUR website!
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=
OR