Quantcast

A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

apple_pi

  • 2 years ago

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

  • This Question is Closed
  1. apple_pi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 7

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

  2. apple_pi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 7

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

  3. cornitodisc
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes,,you're right

  4. apple_pi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 7

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

  5. hartnn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yup, tried that, much interesting ...

  6. apple_pi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 7

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

  7. cornitodisc
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes,,that's right

  8. apple_pi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 7

    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
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 7

    sorry, not √ but ±√

  10. hartnn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    did the same way, good,go on.

  11. apple_pi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 7

    (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
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 7

    And viola, the quadratic formula

  13. hartnn
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Good Work !

  14. apple_pi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 7

    Thank you

  15. ganeshie8
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  16. apple_pi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 7

    Your welcome

  17. lgbasallote
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    not satisfied with the completing the square solution huh?

  18. apple_pi
    • 2 years ago
    Best Response
    You've already chosen the best response.
    Medals 7

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

  19. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.