## apple_pi 3 years ago NOT A QUESTION (JUST INTERESTING) Alternate derivation of the quadratic formula

1. apple_pi

You may be familiar with the derivation of the quadratic formula by completing the square...

2. apple_pi

We can get the exact same result by using the sum and products of roots

3. cornitodisc

yes,,you're right

4. apple_pi

given a quadratic equation: ax^2+bx+c=0 let the two roots be p and q (which are equal to x)

5. hartnn

yup, tried that, much interesting ...

6. apple_pi

p+q=-b/c pq=c/a

7. cornitodisc

yes,,that's right

8. apple_pi

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

9. apple_pi

sorry, not √ but ±√

10. hartnn

did the same way, good,go on.

11. apple_pi

(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

12. apple_pi

And viola, the quadratic formula

13. hartnn

Good Work !

14. apple_pi

Thank you

15. ganeshie8

Excellent ! somehow ive never seen this before. thank you !!

16. apple_pi

17. lgbasallote

not satisfied with the completing the square solution huh?

18. apple_pi

nah, long at messy.. this way seems so much more elegant