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**demha****Member**- Registered: 2012-11-25
- Posts: 186

I would very much appreciate the help on checking if these are correct

Solve the quadratic equations in questions 1 5 by factoring.

1.

Q. x2 49 = 0

A. x = -7, 7

2.

Q. 3x3 12x = 0

A. x = -2, 2

3.

Q. 12x2 + 14x + 12 = 18

A. x = -3/2, 1/3

4.

Q. x3 + 22x2 121x = 0

A. x = 11, 11

5.

Q. x2 4x = 5

A. x = -1, 5

6.

Q. Work backwards to write a quadratic equation that will have solutions of x = 3 and x = -7.

A. x2 4x - 21

7.

Q. Work backwards to write a quadratic equation that will have solutions of x = 12 and x = 2.

A. x2 14x + 24

8.

Q. Work backwards to write a quadratic equation that will have solutions of x = -1/2 and x = 4.

A. x2 7/2x -2

And if we want to get rid of the fraction:

2(x2 7/2x -2)

2x2 14/2x 2

(2 goes into 14, 7 times)

Final Answer: 2x2 7 - 4

9.

Q. Write a quadratic equation that will have a solution of only x = 0. Note: this means there will be a double solution of x = 0.

A. x2 + 0x + 0

10.

Q. Write a quadratic equation that cannot be factored.

A. x2 + x + 3

11.

Q. The product of two consecutive positive integers is 72. Find the integers.

A.

n(n + 1) = 72

n2 + n = 72

n2 + n 72 = 0

(n + 9)(n 8) = 0

Solution becomes -9 and 8. Problem asks for two positive numbers. We reject -9. Since n = 8 and there is n+ 1, we do 8 + 1 which comes up to 9.

Answer: 8, 9

12.

Q. The product of two consecutive negative integers is 10506. Write a quadratic equation that you could solve to find the integers.

A.

n(n + 1) = 10506

n2 + n = 10506

n2 + n 10506 = 0

(n + 103)(n 102) = 0

Solution comes to an obvious -103 and 102. Problem asks for two negative numbers.

n + 1 = -103 + 1 = -102

Answers: -102, -103

13.

Q. The product of two consecutive odd integers is 63. Write a quadratic equation that you could solve to find the integers, then find the integers.

A.

n(n + 2) = 63

n2 + n = 63

n2 + n 63 = 0

(n + 9)(n 7)

Answer: -9, 7

14.

Q. A tennis ball is launched with an initial velocity of 24.5 m/s from the edge of a cliff that is 117.6 meters above the ground. Which quadratic equation could be used to correctly determine when the ball will hit the ground:

4.9t2 + 24.5t + 117.6 = 0

-4.9t2 - 24.5t + 117.6 = 0

-4.9t2 + 24.5t - 117.6 = 0

4.9t2 + 24.5t - 117.6 = 0

-4.9t2 + 24.5t + 117.6 = 0

A. I believe the last equation is the correct one: -4.9t2 + 24.5t + 117.6 = 0

15.

Q. Solve the equation you chose in question 18 to determine when the ball will hit the ground. (HINT: If you don't get one of the answers listed for this question, then maybe you chose the wrong equation in #18. Use this opportunity to double check your work!)

t = 8 seconds

t = 4 seconds

t = 3 seconds

t = -3 seconds

The ball will never reach the ground.

A. I believe the third one is correct: t = 3 as in it will take 3 seconds for the ball to hit the ground.

16.

Q. Using the same equation, determine when the ball is at a height of 49 meters.

A. It will take 7 seconds for the ball to reach 49 meters.

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,227

Hi;

1) That is correct.

2) Is incorrect.

3) Is correct.

4) Is incorrect.

5) Is correct.

6) Is incorrect.

7) Correct.

8)

Final Answer: 2x2 7 - 4

Missing an x.

9)Correct.

10) Correct.

11) Correct.

12) Correct.

13

(n + 9)(n 7)

Answer: -9, 7

That is incorrect.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

Hi bobbym

Her 4) and 13) are also correct.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,227

Hi;

Four is missing a root? 13 asks for positive numbers.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,518

13) says integers...

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,227

Can't be one positive and one negative.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**demha****Member**- Registered: 2012-11-25
- Posts: 186

anonimnystefy wrote:

Hi bobbym

Her 4) and 13) are also correct.

Hi anonimnystefy,

I'm a guy... so it would be a he, not a she

---

Hi bobyym,

Thanks for answering. I submited my work already though and it seems that all but #6 and #15 are correct (according to my teacher). Right now she wants me to show her the work I have done to get those answers. I believe those two may be wrong.

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,227

Your teacher is not correct but if he/she wants to say you are right then let's leave it alone for now.

6)

Work backwards to write a quadratic equation that will have solutions of x = 3 and x = -7.

The correct equation is,

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**demha****Member**- Registered: 2012-11-25
- Posts: 186

Alright, let me try that my self and please do tell any mistakes I make along the way. I will also try #15.

x = 3 and x = -7

(x 3) (x + 7)

x(x 3)

7(x - 3)

(x^2 3x)

(7x - 21)

When adding together, you are taking away 7x from 3x which becomes -4x. This changes the sign and that means the correct equation is:

x^2 + 4x 21

I see where I made my mistake, I didnt change the sign!

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,376

hi demha,

That is correct.

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**demha****Member**- Registered: 2012-11-25
- Posts: 186

My class shows me how to do #15, this website shows the exact same thing: since I can't post links, search on Google: Using Quadratic Formula to Find the Zeros of a Polynomial and click the first link.

Here are my answers:

-3.30 (round up becomes -3)

1.22 (round up becomes 1)

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,227

Hi;

Did you pick the third equation

as you said?

You know that neither of those answers make any sense. How could the ball hit the ground in 1 second? So either you picked the wrong equation or you did not solve it correctly.

Answers in math ought to make sense. Mine don't but that is only because I work on nonsense.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**demha****Member**- Registered: 2012-11-25
- Posts: 186

Actually it is the last one:

-4.9t^2 + 24.5t + 117.6 = 0

First time I did it, I got a postive 3 in the end and chose that as my answer. I must have made a mistake somewhere then?

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,376

hi demha,

That equation looks right to me but your answers of -3.30 and 1.22 don't work in it.

Are you using the quadratic formula?

You'll need to write your steps if you want someone to find the error.

Have a look at

http://www.mathsisfun.com/quadratic-equ … olver.html

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,227

Actually it is the last one:

-4.9t^2 + 24.5t + 117.6 = 0

Sorry, that is the one I meant. The equation is right but the roots are obviously not. Like I said the ball can not possibly hit the ground in one second so you know something is wrong. The quadratic formula can be a little tricky.

Always plot first, you can see the roots now.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**demha****Member**- Registered: 2012-11-25
- Posts: 186

Hi Bob:

That website shows exactly how I have done it but, obviously I have made some mistake if I did not get my 8.

Hi Bobbym:

Yes, I know it couldn't be -3 (because I am trying to find seconds here, -3 will not be it) and definately would not be 1 second. I'll show you my work using the website Bob has given.

---

-4.9t^2 + 24.5t + 117.6 = 0

-24.5 (sqr)24.5^2 - 4(-4.9)(117.6) / 2(-4.9)

First I did all of the multiplication with parenthesis:

-24.5 (sqr)24.5^2 - 4(-576.24) / -9.8

Then I multiplied the number in the parentheses with 4 and multiplied 24.5^2 by itself:

-24.5 (sqr)600.25 - (-2304.96) / -9.8

Since the number in the parenthesis is a negative and there is a minus, I changed it to a plus:

-24.5 (sqr)600.25 + 2304.96 / -9.8

-24.5 (sqr)2905.21 / -9.8

Now I square the number and create two equations:

-24.5 + 53.9 / -9.8

-24.5 - 53.9 / -9.8

29.4 / -9.8 = -3

-78.4 / -9.8 = 8

It seems as if I got it right this time! It must of been a small mistake I carelessly made along the way. I think I might have divided first, the add/subtract. Thank you for your time and help guys!;)

*Last edited by demha (2012-12-12 18:08:48)*

"The thing about quotes on the Internet is you cannot confirm their validity"

~Abraham Lincoln

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,227

Hi;

Glad you worked it out yourself.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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