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September 30th, 2011, 06:46 AM   #1
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Showing how the quadratic formlar was Derived-do you agree?

The Formula Method of The Quadratic Equation - How It Was Derived
The formula method of the quadratic equation is often a popular request by student. So we have taken our time to break down the steps to how this formula was arrived at.

How the formula method was derived.

The formula method of the quadratic equation can be regarded as a derivative
Of completing the square method of solving the prototype of a quadratic equation.
I.e ax^2 + bx + c = 0

By solving the prototype quadratic equation above ,using completing the square method. We will arrive at the quadratic formula below

(-b +- /b^2-4ac)
Now let's examine how the formula came about.

Take your equation (the quadratic equation prototype)

ax^2 + bx + c = 0

move the constant c in the quadratic equation to the R.H.S of the equation (R.H.S - right hand side)

we have :
ax^2 + bx = -c

now divide through by a

ax^2/a + bx/a = -c/a

we will arrive at :

x^2 + bx/a = -c/a

applying Completing the square method

x^2 + bx/a + (b/2a)^2 = - c/a + (b/2a)^2 ---------(1)

from the above equation,it could be pictured that half the co-efficient of x (of bx/a) which is b/2a was squared and added to to both sides of the equation.(That is what we call completing the sqare method of the quadratic equation)

by solving equation (1):

we will have,

(x+b/2a)^2 = b^2/4a^2 - c/a

{note that (x+b/2a)^2 when expanded is the same as x^2 + bx/a +(b/2a)^2 }

Acting on the R.H.S of the equation,

(x+b/2a)^2 = b^2 - 4ac

taking the square root of both sides we have,

x + b/2a = +-/b^2 - 4ac

now solving for x we have,

X= -b/2a +- /b^2 - 4ac
which could further be simplified as

X= -b+-/b^2-4ac

i.e. X= -b+/b^2-4ac or X= -b-/b^2-4ac
2a 2a

That's just how the formula method of quadratic equation was derived.

But there is a better way to solve quadratic equation.You can tell the roots merely by looking at the equations. You can find it [color=#800000]The[/color]
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