What are the 11 General Orders of a Sentry in the US Navy?

[mathdad]

Show that the product of the roots of the equation

x^2 + px + q = 0 is q.

I need help with the set up.

Must I use the discriminant here?

 

[Greg]

Are you sure the product is p? It seems it would be q.

 

[HallsofIvy]

Show that the product of the roots of the equation

x^2 + px + q = 0 is p.

I need help with the set up.

Must I use the discriminant here?

If the roots of the equation are "a" and "b", then we must have (x- a)(x- b)= x^2+ px+ q. What does that tell you about the product of a and b?

 

[mathdad]

Are you sure the product is p? It seems it would be q.

I edited my post. Yes, the product is q.

 

[mathdad]

If the roots of the equation are "a" and "b", then we must have (x- a)(x- b)= x^2+ px+ q. What does that tell you about the product of a and b?

(x- a)(x- b) = x^2+ px+ q

x^2 - ax - bx + ab = x^2 + px + q

x^2 - x^2 -ax - bx - px + ab = q

-ax - bx - px + ab = q

What is next?

 

[Greg]

x^2 - ax - bx + ab = x^2 + px + q

$$x^2-x(a+b)+ab=x^2+px+q\implies a+b=-p,ab=q$$

 

[MarkFL]

Here's another approach:

Suppose we have:

\(\displaystyle ax^2+bx+c=0\)

Then by the quadratic formula, we know the product $P$ of the roots is:

\(\displaystyle P=\left(\frac{-b+\sqrt{b^2-4ac}}{2a}\right)\left(\frac{-b-\sqrt{b^2-4ac}}{2a}\right)=\frac{b^2-b^2+4ac}{4a^2}=\frac{c}{a}\)

In the given problem, we have:

\(\displaystyle a=1,\,c=q\)

Hence:

\(\displaystyle P=\frac{q}{1}=q\quad\checkmark\)

 

[mathdad]

Here's another approach:

Suppose we have:

\(\displaystyle ax^2+bx+c=0\)

Then by the quadratic formula, we know the product $P$ of the roots is:

\(\displaystyle P=\left(\frac{-b+\sqrt{b^2-4ac}}{2a}\right)\left(\frac{-b-\sqrt{b^2-4ac}}{2a}\right)=\frac{b^2-b^2+4ac}{4a^2}=\frac{c}{a}\)

In the given problem, we have:

\(\displaystyle a=1,\,c=q\)

Hence:

\(\displaystyle P=\frac{q}{1}=q\quad\checkmark\)

Great work! If you gave me c/a, I could have taken it from there. Thank you for your help as I travel through David Cohen's precalculus textbook. The textbook questions will get a lot harder in the coming chapters but with your guidance, I'll learn a great deal.

 

[MarkFL]

Great work! If you gave me c/a, I could have taken it from there. Thank you for your help as I travel through David Cohen's precalculus textbook. The textbook questions will get a lot harder in the coming chapters but with your guidance, I'll learn a great deal.

When I took PreCalc back in 1991, it was David Cohen's textbook that we used...third edition. :D

 

[mathdad]

When I took PreCalc back in 1991, it was David Cohen's textbook that we used...third edition. :D

I have David Cohen's precalculus textbook third edition. I purchased the book from amazon.com. It is one of the best precalculus textbooks ever put together.

This may come as a shock to you, but I took precalculus at Lehman College in the Spring 1993 semester as an elective course and got an A minus. My purpose for joining this website is to review precalculus. I love math. I should have majored in math but selected sociology instead.

 

[MarkFL]

I have David Cohen's precalculus textbook third edition. I purchased the book from amazon.com. It is one of the best precalculus textbooks ever put together.

This may come as a shock to you, but I took precalculus at Lehman College in the Spring 1993 semester as an elective course and got an A minus. My purpose for joining this website is to review precalculus. I love math. I should have majored in math but selected sociology instead.

Yes, I think it is a well-written textbook too. (Yes)

When I was taking College Algebra, near the end of the semester I was approached by my professor, and he told me that he would be teaching Analytic Trigonometry during the first summer term and that it would be the last time that course would be taught, as a new course called Pre-Calculus would be taking its place. At that time, Analytic Trigonometry was a course taught between Calc I and II. My professor told me he had gotten a waiver for me regarding the Calc I prerequisite. He said the treatment of trig was more thorough in that course than it would be in Pre-Calc, and that he wanted to give me the chance to experience it.

So, I took the Analytic Trigonometry course during the summer, and then that fall I also took the new Pre-Calc course, so I got a double dose of trigonometry before going into the calculus sequence, which certainly didn't hurt. :D

 

[mathdad]

Yes, I think it is a well-written textbook too. (Yes)

When I was taking College Algebra, near the end of the semester I was approached by my professor, and he told me that he would be teaching Analytic Trigonometry during the first summer term and that it would be the last time that course would be taught, as a new course called Pre-Calculus would be taking its place. At that time, Analytic Trigonometry was a course taught between Calc I and II. My professor told me he had gotten a waiver for me regarding the Calc I prerequisite. He said the treatment of trig was more thorough in that course than it would be in Pre-Calc, and that he wanted to give me the chance to experience it.

So, I took the Analytic Trigonometry course during the summer, and then that fall I also took the new Pre-Calc course, so I got a double dose of trigonometry before going into the calculus sequence, which certainly didn't hurt. :D

Great story. Thanks for sharing. A little more about me. I am 51 (will be 52 next month). Life is like a passing shadow. I will forever regret not majoring in math. Sociology did nothing for me, nothing at all.

Do you know Krista King? Krista is a girl who fell in love with math after majoring in psychology. You can find her math videos on youtube.com. Krista's story is similar to mine. I fell in love with mathematics after earning my B.A. in Sociology. Strange, right?

I graduated from Lehman College in 1994 and had an opportunity to return to college as a math major but decided to enlist in the Navy instead. The internet allows me to learn math for free. I do not have to attend college to learn math or to review courses taken long ago.

 

[MarkFL]

Great story. Thanks for sharing. A little more about me. I am 51 (will be 52 next month). Life is like a passing shadow. I will forever regret not majoring in math. Sociology did nothing for me, nothing at all.

I'm 53, and yes life does seem to pass by more quickly the older I get. :D As a child and young adult, a year seemed to be an eternity...now a year goes by before I know it.

Do you know Krista King? Krista is a girl who fell in love with math after majoring in psychology. You can find her math videos on youtube.com. Krista's story is similar to mine. I fell in love with mathematics after earning my B.A. in Sociology. Strange, right?

I'm not familiar with her story. I had always enjoyed numbers, but I enrolled at my local community college because I had gotten into computer programming and I began to realize that I needed to learn some of that fancy cipherin' with the letters in it...LOL! Once I begna taking math courses, I realized I enjoyed it as much, if not more than, computer programming.

I graduated from Lehman College in 1994 and had an opportunity to return to college as a math major but decided to enlist in the Navy instead. The internet allows me to learn math for free. I do not have to attend college to learn math or to review courses taken long ago.

I served in the U.S. Navy as well, but I went in before any college, as a still wet behind the ears 17 year old. :D

 

[mathdad]

I'm 53, and yes life does seem to pass by more quickly the older I get. :D As a child and young adult, a year seemed to be an eternity...now a year goes by before I know it.
I'm not familiar with her story. I had always enjoyed numbers, but I enrolled at my local community college because I had gotten into computer programming and I began to realize that I needed to learn some of that fancy cipherin' with the letters in it...LOL! Once I begna taking math courses, I realized I enjoyed it as much, if not more than, computer programming.
I served in the U.S. Navy as well, but I went in before any college, as a still wet behind the ears 17 year old. :D

We are close in age.

We were both in the Navy.

We both love math.

Look at my username.

RTCNTC.

RTC = RECRUIT TRAINING COMMAND.

NTC = NAVAL TRAINING CENTER.

 

[MarkFL]

We are close in age.

We were both in the Navy.

We both love math.

Look at my username.

RTCNTC.

RTC = RECRUIT TRAINING COMMAND.

NTC = NAVAL TRAINING CENTER.

Ah, I didn't catch that about your username. I got to enjoy Great Lakes RTC beginning in January...that was some brisk weather to be sure. (Rofl) I took part in a triple-threat company, singing in the Blue Jackets Choir. I surprised the other guys, who had nicknamed me "Professor Peabody" because of my rather large head and "youthful appearance" when I sang bass.

We earned the "Big Chicken" flag each week, and always got to cut to the front of the line in the mess hall. (Yes) Do you remember "Ricky Raisin?"

 

[mathdad]

Ah, I didn't catch that about your username. I got to enjoy Great Lakes RTC beginning in January...that was some brisk weather to be sure. (Rofl) I took part in a triple-threat company, singing in the Blue Jackets Choir. I surprised the other guys, who had nicknamed me "Professor Peabody" because of my rather large head and "youthful appearance" when I sang bass.

We earned the "Big Chicken" flag each week, and always got to cut to the front of the line in the mess hall. (Yes) Do you remember "Ricky Raisin?"

I have forgotten a lot of the Navy terms and slangs. I love gospel quartet music. My favorite bass singer of all time is George Younce who passed away in April 2005. George sang bass for different quartets but he is known for his singing with the Cathedral Quartet from Stow, Ohio.

Good to know that you sang bass for the RTC choir. They always do a great job at each Pass-in-Review. I miss the Navy and my youth. I live in NYC but hate the city lifestyle.
Friends and family think my love for numbers is silly and a complete waste of time.

1. I am not trying to be a math teacher.

2. When my algebra/precalculus skills are a bit more polished, I may decide to become a private math tutor. The extra money is needed considering my current ridiculous salary.

3. At 51 going on 52, dating has become a distant dream.

4. Math keeps my ATTENTION TO DETAIL in good working order.

More precalculus questions tomorrow. Gotta get ready to work.

Can you set up the total areas to equal the given area in the LENGTH OF EACH PIECE OF WIRE problem? I can take it from there.

P.S. The only reason why I do not math tutor now is the fact that word problems kick my behind all the time. I must improve my word problems skills or else tutoring goes out the window.

 

[MarkFL]

"Ricky Recruit" was a nickname applied to recruits in their first week of boot camp...and "Ricky Raisin" was applied to those who didn't yet have access to an iron to remove the wrinkles from their uniforms, and so their wrinkled appearance was reminiscent of a raisin. (Giggle)

I still remember one of our cadences:

Ricky Raisin don't be blue...
My recruiter screwed me too...
Right right, right on...
Boogie down and carry on...

When I first really began getting into math, I would naively try to tell my friends and family about some new concept I was learning, which I found fascinating. Over time I began to see the stifled yawns, dull looks, squirms and quick changes of subject in the conversation, so I quit talking about it with them. (Dull)

 

[mathdad]

"Ricky Recruit" was a nickname applied to recruits in their first week of boot camp...and "Ricky Raisin" was applied to those who didn't yet have access to an iron to remove the wrinkles from their uniforms, and so their wrinkled appearance was reminiscent of a raisin. (Giggle)

I still remember one of our cadences:

Ricky Raisin don't be blue...
My recruiter screwed me too...
Right right, right on...
Boogie down and carry on...

When I first really began getting into math, I would naively try to tell my friends and family about some new concept I was learning, which I found fascinating. Over time I began to see the stifled yawns, dull looks, squirms and quick changes of subject in the conversation, so I quit talking about it with them. (Dull)

I remember the term Ricky Recruit.

Do you recall ROAD GUARDS POST?

HAVE ABOUT THIS SONG?

MAMA, MAMA, CAN'T YOU SEE,
WHAT THE NAVY'S DONE TO ME?
I USED TO DRIVE A CADILLAC,
NOW A SEABAG ON MY BACK.

Here is one of the general orders of the sentry:

To take charge of this post and all government property in view.

More precalculus tomorrow.

- - - Updated - - -

"Ricky Recruit" was a nickname applied to recruits in their first week of boot camp...and "Ricky Raisin" was applied to those who didn't yet have access to an iron to remove the wrinkles from their uniforms, and so their wrinkled appearance was reminiscent of a raisin. (Giggle)

I still remember one of our cadences:

Ricky Raisin don't be blue...
My recruiter screwed me too...
Right right, right on...
Boogie down and carry on...

When I first really began getting into math, I would naively try to tell my friends and family about some new concept I was learning, which I found fascinating. Over time I began to see the stifled yawns, dull looks, squirms and quick changes of subject in the conversation, so I quit talking about it with them. (Dull)

Look what I found:

Learn: US Navy - 11 General Orders of a Sentry (by joshuax) - Memorize.com - Remember and Understand