Solving Quadratics by Factoring and Graphing

bobbym · 2011-08-04 02:18:59

Slightly off. You get two answers to the quadratic as you expected.

8 and -9

We reject the -9 because it is negative. So n = 8. If n = 8 the next number is n+1 which is 8 + 1 = 9.

So your answer is 8 and 9 as the two consecutive positve integers.

zee-f · 2011-08-04 02:24:52

n(n+1)=72

n^2+n-72=0

-72+n+n^2=0

8+-1n=0
8+-8+-1n=0+-8

-1n=-8
n=8

8(8+1)=72

8(9)=72

so thats how am spouse to post it to my teacher right ?

bobbym · 2011-08-04 02:27:57

I would not have left out the factoring that gave the two roots of (8,-9).

Also I would label the answer as the 2 consecutive integers as I did in post # 201 on the bottom.

zee-f · 2011-08-04 02:29:38

(n + -1n)(8 + -1n) = 0

zee-f · 2011-08-04 02:31:13

so i would post all my work to her and add reject the -9 because it is negative

bobbym · 2011-08-04 02:36:20

Yes, always provide as much work as possible. Most teachers are in love with partial credit. Give them every oppurtunity to give you partial credit.

zee-f · 2011-08-04 02:41:28

what about 17

what should i post this

n(n+2)=63

n(2+n)=63

2n+n^2=63

-63+2n+n^2=63+-63

-63+2n+n^2=0
(-9+-1n)(7+-1n)=0

-9+-1n=0
-9+9+-1n=0+9

-1n=9

n=-9

7+-1n=0
7+-7+-1n=0

-1n=-7

n=7

and add what to it ?

bobbym · 2011-08-04 02:42:58

Add two!

zee-f · 2011-08-04 02:47:21

what two

bobbym · 2011-08-04 02:48:04

If 7 is the first number then 9 is then next odd consecutive number. That is 7 + 2 = 9.

zee-f · 2011-08-04 02:49:07

i hate this lesssssssssssson

anonimnystefy · 2011-08-04 02:50:27

well you shouldn't this one has a lot of use in the future.

bobbym · 2011-08-04 02:51:15

Hate it? Why? Solving word problems is necessary and you are doing okay.

zee-f · 2011-08-04 03:03:36

no i think am doing horrible in the word problems

bobbym · 2011-08-04 03:04:10

So? That is the purpose of the forum, to help you get better.

zee-f · 2011-08-04 05:27:14

yeah i am getting alllot more better in math than to the forum

bobbym · 2011-08-04 05:30:29

Hi;

Are you all done?

zee-f · 2011-08-04 05:39:40

do you think this is the correct way to get the integer ?

1-Call the smallest unknown integer of the consecutive set "n" and call the following integers "n+1," "n+2" and so on for as many integers there are in the set. For example, if the subject of an SAT question is a set of four consecutive positive integers, call them "n," "n+1," "n+2" and "n+3."

2
Plug the variables into the given algebraic equation. For instance, if the SAT question states that the sum of the squares of four consecutive positive integers is 126, you set up the equation n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 = 126.

3
Simplify the equation and solve for "n." For example, you can simplify the equation n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 = 126 to 4n^2 + 12n^2 - 112 = 0 by expanding the squared expressions and combining like terms.

If you use your calculator or the quadratic formula, you will find the two solutions are n = 4 and n = -7. Since the question restricts you to positive integers only, you can disregard n = -7. Therefore the smallest integer in the set is 4.

4
Use the value of "n" to find the rest of the integers in the set. Following the example, if n = 4, then the other numbers are 5, 6 and 7.

5
Use the values of the consecutive integers to answer the main question in the SAT problem. For example, suppose the full question is "The sum of the squares of four consecutive positive integers is 126. What is the product of the four integers?" Since the four consecutive integers are 4, 5, 6 and 7, and 4*5*6*7 = 840, the answer to this problem is 840

zee-f · 2011-08-04 05:41:18

yup am done

bobbym · 2011-08-04 05:42:01

Hi;

1) That is one way of doing it. Since there are other ways you can not say that is the correct way.

2) Again that is one way of doing it.

zee-f · 2011-08-05 06:04:13

hey i just wanted to make sure here its asking for two negative integers so wouldn't the next one be -101 ? because -103+2=-101 ???

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

16- n(n+1)=10506

n^2+n-10506=0

-10506+1n+n^2=10506+-10506

-10506+1n+n^2=0

(-103+-1n)(102+-1n)=0

-103+-1n=0

-1n=0+103

-1n=103

n=-103

102+-1n=0

102+-102+-1n=0+-102

-1n=0+-102

-1n=-102

n=102

bobbym · 2011-08-05 06:08:59

You would now pick the -103. The next consecutive negative integer is - 102.

As you can see the answer has got to be 10506. If n = - 103 then n + 1 = - 102.

zee-f · 2011-08-06 01:50:45

hey this is what my teacher said about my work

#2. How did you solve -2 + x = 0.

#6. When you have (x +3)(x + 4), how did you solve that and get -4, -1?

12. Good. When we have a problem that contains a fraction, we will multiply the equation by the denominator to remove the fraction. Try this please.

bobbym · 2011-08-06 01:52:27

Yes, #6 is wrong. It should be -3 and - 4

So you have worked on about 1100 problems and only got 3 wrong. I should do as well!

zee-f · 2011-08-06 02:36:12

am sure you would do much better than i do but why is #6 wrong ??

Math Is Fun Forum

#201 2011-08-04 02:18:59

Re: Solving Quadratics by Factoring and Graphing

#202 2011-08-04 02:24:52

Re: Solving Quadratics by Factoring and Graphing

#203 2011-08-04 02:27:57

Re: Solving Quadratics by Factoring and Graphing

#204 2011-08-04 02:29:38

Re: Solving Quadratics by Factoring and Graphing

#205 2011-08-04 02:31:13

Re: Solving Quadratics by Factoring and Graphing

#206 2011-08-04 02:36:20

Re: Solving Quadratics by Factoring and Graphing

#207 2011-08-04 02:41:28

Re: Solving Quadratics by Factoring and Graphing

#208 2011-08-04 02:42:58

Re: Solving Quadratics by Factoring and Graphing

#209 2011-08-04 02:47:21

Re: Solving Quadratics by Factoring and Graphing

#210 2011-08-04 02:48:04

Re: Solving Quadratics by Factoring and Graphing

#211 2011-08-04 02:49:07

Re: Solving Quadratics by Factoring and Graphing

#212 2011-08-04 02:50:27

Re: Solving Quadratics by Factoring and Graphing

#213 2011-08-04 02:51:15

Re: Solving Quadratics by Factoring and Graphing

#214 2011-08-04 03:03:36

Re: Solving Quadratics by Factoring and Graphing

#215 2011-08-04 03:04:10

Re: Solving Quadratics by Factoring and Graphing

#216 2011-08-04 05:27:14

Re: Solving Quadratics by Factoring and Graphing

#217 2011-08-04 05:30:29

Re: Solving Quadratics by Factoring and Graphing

#218 2011-08-04 05:39:40

Re: Solving Quadratics by Factoring and Graphing

#219 2011-08-04 05:41:18

Re: Solving Quadratics by Factoring and Graphing

#220 2011-08-04 05:42:01

Re: Solving Quadratics by Factoring and Graphing

#221 2011-08-05 06:04:13

Re: Solving Quadratics by Factoring and Graphing

#222 2011-08-05 06:08:59

Re: Solving Quadratics by Factoring and Graphing

#223 2011-08-06 01:50:45

Re: Solving Quadratics by Factoring and Graphing

#224 2011-08-06 01:52:27

Re: Solving Quadratics by Factoring and Graphing

#225 2011-08-06 02:36:12

Re: Solving Quadratics by Factoring and Graphing

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