This could be big.
But, only in bank employees, sadly.
Maybe weâll all be tripping
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This came up in my feed today. An interesting approach to factoring quadratic equations. It claimed to be simpler than usual methods and remove âguess and checkâ. It actually ended up being pretty clever.
4 minute video, first half is âinspirationâ, second half shows the method:
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It doesnât seem any easier than using the formula. More steps, actually.
The point is, you donât need to memorize a formula for it.
True, but one needs to memorize the process.
And, one can always solve the formula if one forgets. Solve it enough times, one will remember the formula.
Also, this method only works when A = 1. Is there an âeasy wayâ to solve when A <> 1? I WANT MY 2 MINUTES BACK!
Nice that B was an even number in his example. Suppose it is 7 (keep C = 12).
Now,
step 1: let a = factor 1 = 3.5 - u; let b = factor 2 = 3.5 + u
step 2: multiply a and b; ok, 3.5^2 - u^2 = 12. Great, this isnât difficult at all! Lucky me that squared factors of 5 make this 3.0 * 4.0 + 0.25 = 12.25. So u^2 = 0.25. and u = ± 0.5.
So, a = 3, b = 4.
Easier to list the factors of C, see which ones add to B. One will note that starting from {1, C} and increasing the first factor, the sums get smaller. If you go past B, there are no rational solutions.
The YT video did say it was a âdifferent wayâ not easier, so, this belongs in the âho-hum scienceâ thread.
Proof of odd squared factors of 5: Let natural number A = 10 * B + 5.
A^2 = 100 * B ^ 2 + 100 * B + 25.
= 100 * (B) * (B + 1) + 25
= (10 * B) * ((10 * (B + 1)) + 25.
10 * B is the factor of 10 below A, ((10 * (B + 1)) is the factor of 10 above A.
QED
Divide by A first?
One nice thing about his method is that it also finds irrational solutions, unlike guess and check.
Iâm not claiming its groundbreaking or anything, but I can certainly see it making intuitive sense to kids, as opposed to memorizing the quadratic formula or completing the square.
Factoring quadratics is for math students .
Well, it is a way for kids to think, âYeah, that formula works every time; I think Iâll use that instead.â
This method is completing the square.
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Agree. It is.