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Imparcticle
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http://mathworld.wolfram.com/QuadraticFormula.html
Why is the alternate form the way it is? why is 2c the numerator and not 2a?
Why is the alternate form the way it is? why is 2c the numerator and not 2a?
JohnDubYa said:It also has to do with the number of operations you have to perform...
StonedPanda said:If your value of C is off by 0.5, then in f your answer will be off by 1, but in g your answer will be off by less than one.
Or, if you know each coefficient exactly, but they're way too long to compute with, depending on where you enter them into the formula, your forced rounding will matter less.
That's just my guess, anyway.
so instead of computing you compute
What's round-off error? I'm guessing "low order" refers to the order of polynomials?Each term introduces round-off error, so the trick is to get an accurate representation at low order
arildno said:Multiply the usual form with
[tex]1=\frac{-b\mp\sqrt{b^{2}-4ac}}{-b\mp\sqrt{b^{2}-4ac}}[/tex]
Edited a small mistake
(Usual form:[tex]\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}[/tex])
Computers typically work in base 2. For the point of illustration, assume you are working with a computer that uses base 10 for floating point arithmetic and assume it only has 5 significant digits. For example, computing 1.0/3.0 and 200.0/3.0 on this computer yields 0.33333 and 66.667, respectively. Now suppose you need to find the solutions toImparcticle said:why doesn't the computer run them the same?
The alternate form of the quadratic formula is x = (-b ± √(b^2 - 4ac)) / 2a.
The alternate form of the quadratic formula is derived from the standard form, x = (-b ± √(b^2 - 4ac)) / 2a, by simplifying the numerator and denominator.
The alternate form of the quadratic formula should be used when solving quadratic equations that have complex or irrational solutions. It is also useful when graphing quadratic functions.
One advantage of the alternate form of the quadratic formula is that it is simpler and more compact than the standard form. It also allows for easier calculation of complex solutions.
Yes, the alternate form of the quadratic formula can be used for all quadratic equations, as long as the equation is in the form of ax^2 + bx + c = 0.