## Hello my friends in bloggyland

## Happy New Year, to you all!

I am sat here at the computer, my little *CAL is playing wii fit plus on her wii fit balance board. She was so excited about getting this, she has told me that it will improve her gross motor skills and she is so into it.

She even got me to have a go and put all my info in….it’s evil, I have decided.

My little mii avatar looks like a blob of custard on legs now….lol

**NOTE: ** to self….new year’s resolution, lose some weight Lisa!!!

### My *AJ is sat behind me revising for his AS levels.

He has been sat at the dining room table constantly revising so hard over the holiday, he is so dedicated to whatever he chooses to do.

I am so very proud of him.

## I just have to share this

I am so grateful for the technology our Aspie kids have got today. *AJ was stuck with a Mathematical problem and there is no way I could possible help him. He went onto **YAHOO! ANSWERS **and within minutes there were two wonderful people there to help him. This is what I witnessed and I will say it moved me to tears. I am so pleased that my Aspie children will have opportunities to do the things they are good at.

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## *AJ’s QUESTION

### Right ok, I’m doing my AS level maths and this kind of thing is something I really just don’t get.

### What does it even mean when it says (k+1)x^2?

Could somebody help me with this showing the working out and maybe explaining it a little so I can work out how to do this question and ones like it.

Oh yes, what is this topic even called? When I look up quadratic equations in the text book it just comes up with something completely different!

Please HELP! Thank you.

**The quadratic equation (k+1)x^2 + 4kx + 9 = 0 has real roots.?**

(a) Show that 4k^2 – 9k – 9 (is larger or equal to) 0.

(b)Hence find the possible values of k

** **

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### ANSWER from. Captain Matticus

In a quadratic equation of:

a * m^(2t) + b * m^t + c = 0

m^t = (-b +/- sqrt(b^2 – 4ac)) / (2a)

if b^2 – 4ac > 0, then there are 2 real roots

if b^2 – 4ac = 0, then there is 1 real root

if b^2 – 4ac < 0, then there are 2 imaginary roots

m^t = x^1

a = k + 1

b = 4k

c = 9

b^2 – 4ac =

16k^2 – 4 * 9 * (k + 1) =

16k^2 – 36k – 36 =

4 * (4k^2 – 9k – 9)

4 * (4k^2 – 9k – 9) >/= 0

4k^2 – 9k – 9 >/= 0

We just use the quadratic equation again to find the roots of k:

k = (9 +/- sqrt(81 + 4 * 4 * 9)) / 8

k = (9 +/- sqrt(9 * 9 + 9 * 16)) / 8

k = (9 +/- sqrt(9 * (9 + 16)) / 8

k = (9 +/- sqrt(9 * 25)) / 8

k = (9 +/- 3 * 5) / 8

k = (9 +/- 15) / 8

k = 24/8 , -6/8

k = 3 , -3/4

So, for all values of k, except when:

-3/4 </= k </= 3

(k + 1) * x^2 + 4 * k * x + 9 has real roots

-infinity < k < -3/4

3 < k < infinity

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### ANSWER from HD_is_aw…

First we need to see , it has real roots

(k+1)x^2 + 4kx + 9 = 0

We check it by , b^2 – 4ac = 0

a = k + 1

b= 4k

c = 9

(4k)^2 – 4 ( k+1) * 9 = 0

16k^2 – 36k – 36 =0

4 ( 4k^2 – 9k – 9) = 0

4k^2 – 9k – 9 = 0

4k^2 -12k + 3k – 9=0

4k ( k – 3) + 3 ( k -3)= 0

(4k + 3)(k – 3) = 0

SO,

4k +3 = 0 => k = -3/4

or

k – 3 = 0 => k = 3

It is the answer of second part of question .

_________-

a) 4k^2 – 9k – 9

if we take value of -3/4

4 ( -3/4)^2 – 9 * (-3/4) – 9

= 4 * 9/16 + 27/4 – 9

= 9/4 + 27/4 – 9

=9 + 27 -36 / 4

= 0/4

= 0

if we take value of 3

4 ( 3)^2 – 9 * (3) – 9

4 * 9 – 27 – 9

36 – 36 = 0

So , our first part is also proved that it will be equal to or greater than 0..!

Hope you would have understood..! Enjoy..! ðŸ˜€

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Happy New Year to you and yours….may the year bring to you all life’s wonderful blessings.

Thank you slp…xx ðŸ™‚

Pingback: Wii fit + Quadratic Equations Â« Alienhippy's Blog

Wow, that sort of hurts my eyes, but I’m glad he got the info he needed!

Happy New Year. ðŸ™‚

hurts my eyes too. Thank you for you comment. xx ðŸ™‚

Oh my!

That’s hurt my head just looking at it!

Sheesh!

Fi…It was TOTALLY wonderful, *AJ was so stuck and he just tapped in his question and within minutes these two amazing people solved his problem. It was a AHA moment for him, he knew exactly what he needed to do. I was in tears, I am so glad our kids have got computers and I don’t have to stress about my lack of education.

I Love you my friend. xxxx

Hi Lisa,

I’m with Fi and Aspergirlmaybe on this. Glad *AJ can read it!

Yes, computers do bring help and friendship, especially in Aspie Bloggyland!

A very Happy New Year to you and all your family.

Bruce ðŸ™‚

I’m glad *AJ can read it too, he has his exam today.

Thank you for you comment Bruce. xx ðŸ™‚

And Wolfram Alpha visualises all these real roots.

So happy I discovered you this year!

I see both answers were step by step and probably easily replicable.

It was also really interesting reading about what your avatar gets up to on the Wii.

Giggle, my avatar is fat and lazy. She is asleep standing up…lol

Ow! That hurt! Clever *AJ just for taking the subject in the first place. Isn’t the internet wonderful??

Happy New Year to all of you ðŸ™‚

Tilly, the internet is more than wonderful!! xx ðŸ™‚

Gosh, why didn’t you ask me, I knew the answer!! “It;’s made my brain hurt just reading the question and the answers haven’t really helped me. I will have to read it again and again and again. Love from Auntie Alberta Einstein xxxx

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I’m glad Cal like’s her Wii Fit Plus. It should be a great help. Lotsa Love xxxx

ðŸ˜‰

Holy macaroni – I now know why I did NOT like Math at school ðŸ˜€

Thanks for wishing me a Happy birthday Lisa ðŸ˜€ I’m not overly hung up about my age, I just posted the little Haiku for fun – haha… !!!!

Love you loads,

Chloe xx

Hello Chloe,

Your Haiku was fun…tell me again, what is a Haiku???

Love and hugs.

xXx

Hi Lisa ðŸ˜€

Well, as far as I know, Haiku is a Japanese form of poetry dating back centuries. The type I write doesn’t exactly follow the Haiku rules but is more a westernised version…which is made up of three lines only…the first and last line having only 5 syllables and the middle line having exactly 7 syllables.

It’s quite fun – you should try it. The key (and fun part) is in trying to convey a whole message in so few words…

Lots of love,

Chloe xx

So glad the help was available and so quickly. I know there was a point in life when I could do math, but that made my head hurt, too. My hubby still remembers everything, but he is an engineer and actually finds it fun:).

After hubby got on our new Wii fit and I saw what his avatar looked like, I decided right then and there to never set foot on it! It really is evil ðŸ™‚

Hi, yes…I was really good at maths at school, this however is a total puzzle to me.

Love and hugs.

xx ðŸ™‚