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The essence of the proof is simply to complete the square for a generalised quadratic equation. Like this:
ax2 + bx + c = 0
Take 'a' outside:
a[x2 + bx/a + c/a] = 0
Divide through by 'a':
x2 + bx/a + c/a = 0
Complete the square:
(x + b/2a)2 - b2/4a2 + c/a = 0
Rearrange to find x:
(x + b/2a)2 = b2/4a2 - c/a
x + b/2a = (+/-)sqrt[b2/4a2 - c/a]
x = -b/2a (+/-) sqrt[b2/4a2 - c/a]
Finally, fiddle around so that (1/2a) can be taken out as a common factor:
x = -b/2a (+/-) sqrt[b2/4a2 - 4ac/4a2]
x = -b/2a (+/-) sqrt[(1/4a2)(b2 - 4ac)]
x = -b/2a (+/-) sqrt(1/4a2)sqrt(b2 - 4ac)
x = -b/2a (+/-) (1/2a)sqrt(b2 - 4ac)
x = [ -b (+/-) sqrt(b2 - 4ac) ] / 2a.
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What is the difference between quadratic formula and quadratic equation?
There are an infinite number of different quadratic equations. The quadratic formula is a single formula that can be used to find the pair of solutions to every quadratic equation.
Is it OK to use the quadratic formula if the given quadratic trinomial is not factorable?
Well, if the given quadratic equation cannot be factored, nor completed by the square, try using the quadratic formula.
What did you choose completing the square or quadratic formula and why?
Quadratic formula. It's easier to remember and you have to do less work.
Solve this quadratic equation using the quadratic formula?
For any quadratic ax2 + bx + c = 0 we can find x by using the quadratic formulae: the quadratic formula is... [-b +- sqrt(b2 - 4(a)(c)) ] / 2a
What are the solutions to the quadratic formula?
The quadratic formula is x=-b (+or-) square root of b2-4ac all over 2a
What is the quadratic formula for?
The quadratic formula is used to solve the quadratic equation. Many equations in which the variable is squared can be written as a quadratic equation, and then solved with the quadratic formula.
Aryabhatta's quadratic formula's?
aryabhatt's quadratic formula
What is the difference between quadratic formula and quadratic equation?
There are an infinite number of different quadratic equations. The quadratic formula is a single formula that can be used to find the pair of solutions to every quadratic equation.
What formula name that gives the solutions for x in a quadratic equation?
This formula is called the quadratic formula.
When do you use the Quadratic Formula in math?
you use the quadratic formula in math when the quadratic equation you are solving cannot be factored.
Grade level of quadratic formula?
8th grade upto college will study the quadratic Formula. ~ I'm in the 6th grade and I study the quadratic formula...
Is the quadratic formula used in Europe equivalent to the quadratic formula used in America?
Yes.
What is the origin of the quadratic formula?
The quadratic formula is derived by completing the square. That is as much as I can tell you.
Is it OK to use the quadratic formula if the given quadratic trinomial is not factorable?
Well, if the given quadratic equation cannot be factored, nor completed by the square, try using the quadratic formula.
What is quadratics or the quadratic formula?
The quadratic formula is: Image Source: http://2.bp.blogspot.com/_V8KsSIiGjBk/SsACMEj73KI/AAAAAAAAFIU/vNtErLdchMw/s1600/Quadratic+Formula.gif
What did you choose completing the square or quadratic formula and why?
Quadratic formula. It's easier to remember and you have to do less work.
Solve this quadratic equation using the quadratic formula?
For any quadratic ax2 + bx + c = 0 we can find x by using the quadratic formulae: the quadratic formula is... [-b +- sqrt(b2 - 4(a)(c)) ] / 2a
