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NOT A QUESTION (JUST INTERESTING) Alternate derivation of the quadratic formula

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You may be familiar with the derivation of the quadratic formula by completing the square...
We can get the exact same result by using the sum and products of roots
yes,,you're right

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Other answers:

given a quadratic equation: ax^2+bx+c=0 let the two roots be p and q (which are equal to x)
yup, tried that, much interesting ...
p+q=-b/c pq=c/a
yes,,that's right
What if we found p-q? (p-q)^2 = p^2 - 2pq + q^2 = (p^2 + q^2) - 2pq = (p+q)^2 - 2pq - 2pq = (p+q)^2 - 4pq = b^2/a^2 - 4*c/a = (b^2-4ac)/a^2 therefore p-q = √(b^2-4ac) /a
sorry, not √ but ±√
did the same way, good,go on.
(p+q)+(p-q)=2p=2x (because a root is a solution of x) 2x = -b/a + √(b^2-4ac) /a x = -b±√(b^2-4ac) ------------- 2a
And viola, the quadratic formula
Good Work !
Thank you
Excellent ! somehow ive never seen this before. thank you !!
Your welcome
not satisfied with the completing the square solution huh?
nah, long at messy.. this way seems so much more elegant

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