Factoring vs. original equation

  • Context: High School 
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Discussion Overview

The discussion revolves around solving the quadratic equation x^2 - 7x + 12 = 0, specifically focusing on the process of factoring the equation and verifying the solutions obtained. Participants explore the implications of the solutions and the importance of correctly substituting them back into the original equation.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about the solutions obtained from factoring the equation, stating that plugging them back into the original equation does not yield zero.
  • Another participant asserts that the solutions of 3 and 4 are correct and suggests that the issue lies in the participant's method of checking the solutions.
  • A different participant humorously suggests that the correct answers might actually be -3 and -4, indicating a potential misunderstanding of the factoring process.
  • Some participants encourage the original poster to double-check their calculations and provide assistance if needed.

Areas of Agreement / Disagreement

There is a general agreement among participants that the solutions of 3 and 4 are correct, but there is disagreement regarding the method of verification and the potential for error in checking those solutions.

Contextual Notes

Participants highlight the importance of correctly substituting values back into the equation and the potential for errors in calculation, particularly with the use of calculators and brackets.

Who May Find This Useful

Students learning about quadratic equations, factoring techniques, and the verification of solutions in algebra.

stnbtch15
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ok so i was presented with the equation x^2-7x+12=0 and i can't decide what the answer should be. if i factor the equation i come up with 3 and 4. but when i plug those back into the original equation it doesn't work. so does that mean that there is no answer or does it mean I'm doing something wrong?
 
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It means you're calculating the values you plugged back into the equation incorrectly :-p

3 and 4 are the correct answers, so try plugging them in once more, and if you still aren't getting zero after plugging in those values, post what you've done so we can help show you what you've done wrong (even if you used a calculator, show us exactly how you wrote it in the calculator because the misuse of brackets can screw up a lot of people).
 
well now i feel like a dummy
 
Happens all the time :smile: - but... you don't... do it all the time do you?

Haha good luck with those quadratics :wink:
 
Um. You mean -3 and -4.
 
Phrak, best you go back and revise your quadratics as well :-p
 
I agree. The OP arrived at the correct solutions, but made a mistake in checking them.
 
Mentallic said:
Phrak, best you go back and revise your quadratics as well :-p

Oh my! You got me.
 

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