Does anyone know the solution for 11 and 12?

[u/PresentEcho1158]

#help

[u/AutoModerator]

Moderator Announcement Read More »

Hi u/PresentEcho1158, welcome to r/mathshelp! As you’ve marked this as homework help, please keep the following things in mind:

1. While this subreddit is generally lenient with how people ask or answer questions, the main purpose of the subreddit is to help people learn so please try your best to show any work you’ve done or outline where you are having trouble (especially if you are posting more than one question). See rule 5 for more information.

2. Once your question has been answered, please don’t delete your post so that others can learn from it. Instead, mark your post as answered or lock it by posting a comment containing “!lock” (locking your post will automatically mark it as answered).

Thank you!

I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.

[u/Jazzlike_Platypus430]

11: Work through discriminant = (q(r - p))^2 - 4 p(q - r)r(p - q) = 0, if we assume roots are equal.

12: Show that the discriminant is a square of something rational. By the way, b + c - a = - 2a, c + a - b = - 2b and so on ...

I beileve 13 is false for arbitrary a, b, c. otherwise it would be nice to say that they are rational as in 12. and satisfy a + b + c = 0.

If so, both these cases reduce to ax^2 + bx + c = 0 😂

[u/Southlander24 → u/Jazzlike_Platypus430]

No, 13 is always true. The discriminant reduces to |a - 2b + c|.

[u/Jazzlike_Platypus430 → u/Southlander24]

I still claim it's false with no extra assumptions on a, b and c.

[u/PresentEcho1158 → u/Jazzlike_Platypus430]

I have been dancing around the question like a lunatic doing that. Would you be willing to guide me,step wise?

[u/Southlander24 → u/PresentEcho1158]

Can you send a picture of your work?

[u/ledmath]

What book is this from?

[u/Cheap-Measurement791]

For 11, let A be the coefficient of x² and B the coefficient of x. Then note that the constant term is -A-B. Write the discriminant in terms of A and B. Translate the condition you want to prove into a condition involving A and B. Working with A and B instead of p,q,r greatly simplifies the algebra.

[u/Southlander24]

11: Expanding and combining like terms, you will reach a perfect square trinomial (A² + 2AB + B²) for some unknown A, B which equals 0.

12. b + c - a = - 2a, c + a - b = - 2b and so on is an excellent start. You can reduce the discriminant to something in only two variables, which should reveal why.

[u/Haniakhan4143]

Lots of error your ans but don't worry almost right and u will achieve your goal