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apple_pi
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NOT A QUESTION (JUST INTERESTING)
Alternate derivation of the quadratic formula
 2 years ago
 2 years ago
apple_pi Group Title
NOT A QUESTION (JUST INTERESTING) Alternate derivation of the quadratic formula
 2 years ago
 2 years ago

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apple_pi Group TitleBest ResponseYou've already chosen the best response.7
You may be familiar with the derivation of the quadratic formula by completing the square...
 2 years ago

apple_pi Group TitleBest ResponseYou've already chosen the best response.7
We can get the exact same result by using the sum and products of roots
 2 years ago

cornitodisc Group TitleBest ResponseYou've already chosen the best response.0
yes,,you're right
 2 years ago

apple_pi Group TitleBest ResponseYou've already chosen the best response.7
given a quadratic equation: ax^2+bx+c=0 let the two roots be p and q (which are equal to x)
 2 years ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
yup, tried that, much interesting ...
 2 years ago

apple_pi Group TitleBest ResponseYou've already chosen the best response.7
p+q=b/c pq=c/a
 2 years ago

cornitodisc Group TitleBest ResponseYou've already chosen the best response.0
yes,,that's right
 2 years ago

apple_pi Group TitleBest ResponseYou've already chosen the best response.7
What if we found pq? (pq)^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^24ac)/a^2 therefore pq = √(b^24ac) /a
 2 years ago

apple_pi Group TitleBest ResponseYou've already chosen the best response.7
sorry, not √ but ±√
 2 years ago

hartnn Group TitleBest ResponseYou've already chosen the best response.1
did the same way, good,go on.
 2 years ago

apple_pi Group TitleBest ResponseYou've already chosen the best response.7
(p+q)+(pq)=2p=2x (because a root is a solution of x) 2x = b/a + √(b^24ac) /a x = b±√(b^24ac)  2a
 2 years ago

apple_pi Group TitleBest ResponseYou've already chosen the best response.7
And viola, the quadratic formula
 2 years ago

ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
Excellent ! somehow ive never seen this before. thank you !!
 2 years ago

apple_pi Group TitleBest ResponseYou've already chosen the best response.7
Your welcome
 2 years ago

lgbasallote Group TitleBest ResponseYou've already chosen the best response.0
not satisfied with the completing the square solution huh?
 2 years ago

apple_pi Group TitleBest ResponseYou've already chosen the best response.7
nah, long at messy.. this way seems so much more elegant
 2 years ago
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