What mistake did Mindy make when solving this quadratic equation?

In summary, Mindy sets x+4=8 and x-3=8 to get x=4. She checks her answer by substituting x=4 into the original equation and finds that it works. She concludes that this quadratic equation has only one solution. If she checks x=-5, it also works. She lost a solution.
  • #1
halvizo1031
78
0

Homework Statement


Mindy solves the problem (x+4)(x-3)=8 by setting x+4=8 and x-3=8, thereby getting the solutin x=4 from both equations. she checks her answer by substituting x=4 into the original equation and finds that it works. She concludes that this quadratic equation has only one solution. if we check x=-5, it also works. she lost a solution. WHAT MISTAKE DID MINDY MAKE? WHAT MIGHT SHE NOT UNDERSTAND? WHAT PROPERTY OF FIELDS/INTEGRAL DOMAINS IS MINDY'S MISTAKE RELATED TO?


Homework Equations





The Attempt at a Solution


If she were to first FOIL, subtract 8 from both sides, and solve for x, then she would get both solutions. BUT, i am stuck in explaining what she might not understand and what fields/integral domains is her mistake related to...
 
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  • #2
I'm thinking that this has to do with Zero Divisors. Specifically the nonexistence of them. Does that help?
 
  • #3
that makes sense as far as explaining her misunderstanding...but what about the property of fields/integral domains that her mistake is related to?
 
  • #4
Mindy is assuming "if ab= c then a= c or b= c" which is not true. It is a mistaken version of the "zero product" rule that says "if ab= 0 then a= 0 or b= 0". That, in turn is true because if [itex]a\ne 0[/itex] we can divide by it getting b= 0 and the reverse. That is where "no zero divisors" in a field is applied and where Mindy's mistake is. "No zero divisors" does NOT mean "no c divisors" for c non-zero.
 
  • #5
halvizo1031 said:

Homework Statement


Mindy solves the problem (x+4)(x-3)=8 by setting x+4=8 and x-3=8, thereby getting the solutin x=4 from both equations.

Um, you don't get x=4 from both equations. If x-3=8, x=11, not 4.
 
  • #6
ideasrule said:
Um, you don't get x=4 from both equations. If x-3=8, x=11, not 4.
Yeah, but by this time Mindy is so lost, it doesn't matter!
 
  • #7
you are correct that she "should" get 4 and 11 but i guess it doesn't matter since her process and reasoning is incorrect. unless the professor made a mistake in typing this question...thank you both for your input.
 

What are the most common types of student errors?

The most common types of student errors include calculation errors, misunderstanding of concepts or instructions, careless mistakes, and lack of attention to detail.

Why is it important to address student errors?

Addressing student errors is important because it helps students to learn from their mistakes and improve their understanding of the subject. It also allows teachers to identify areas where students may be struggling and provide additional support.

How can teachers effectively address student errors?

To effectively address student errors, teachers should provide constructive feedback and opportunities for students to correct their mistakes. It is also important for teachers to understand the root cause of the error and provide targeted instruction to address it.

What strategies can be used to prevent student errors?

Some strategies that can help prevent student errors include providing clear instructions, breaking down complex concepts into smaller, manageable parts, and encouraging students to check their work for accuracy before submitting it.

How can addressing student errors impact student learning?

Addressing student errors can have a positive impact on student learning by promoting a growth mindset, improving critical thinking skills, and increasing student engagement and motivation. It can also help students to develop a better understanding of the subject and improve their overall academic performance.

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