3 hard algebra problems!

**xxravenxx** · October 18th 2009, 10:37 PM

Just can't figure out these 3 problems:

Anyone help please?

Thanks.

**mathaddict** · October 18th 2009, 11:15 PM

Originally Posted by xxravenxx

Just can't figure out these 3 problems:

Anyone help please?

Thanks.

HI

For the first problem ,

$x^2+ax-b=0$ its roots are a and c

$a+c=-a$ ---1

$ac=-b$ ----2

$x^2+cx+d=0$ its roots are b and d ,

$b+d=-c$ --- 3

$bd=d$ ---4

From 4 , $bd=d\Rightarrow b=1$

From 1 , $2a=-c$

At 2 , $a(-2a)=-b$

$2a^2=b$

$2a^2=1$

$a=\pm\frac{1}{\sqrt{2}}$

At 1 , $2(\pm\frac{1}{\sqrt{2}})=-c$

$c=2(\mp\frac{1}{\sqrt{2}})$

$c=\mp\sqrt{2}$

Then , from 2 ,

$1+d=-c$

$1+d=\pm\sqrt{2}$

$<br /> d=-1\pm\sqrt{2}<br />$

**xxravenxx** · October 18th 2009, 11:23 PM

Originally Posted by mathaddict

HI

For the first problem ,

$x^2+ax-b=0$ its roots are a and c

$a+c=-a$ ---1

$ac=-b$ ----2

$x^2+cx+d=0$ its roots are b and d ,

$b+d=-c$ --- 3

$bd=d$ ---4

From 4 , $bd=d\Rightarrow b=1$

From 1 , $2a=-c$

At 2 , $a(-2a)=-b$

$2a^2=b$

$2a^2=1$

$a=\pm\frac{1}{\sqrt{2}}$

At 1 , $2(\pm\frac{1}{\sqrt{2}})=-c$

$c=2(\mp\frac{1}{\sqrt{2}})$

$c=\mp\sqrt{2}$

Then , from 2 ,

$1+d=-c$

$1+d=\pm\sqrt{2}$

$<br /> d=-1\pm\sqrt{2}<br />$

Thank you for giving the solution to Problem 4, however, could you please explain how you got that sign? I don't understand how you got from this:

At 1 , $2(\pm\frac{1}{\sqrt{2}})=-c$

to this:

$c=2(\mp\frac{1}{\sqrt{2}})$

I have never come across that symbol before. Care to explain what it means please?

And any one have solutions for the other two questions?

**mathaddict** · October 18th 2009, 11:27 PM

Originally Posted by xxravenxx

Thank you for giving the solution to Problem 4, however, could you please explain how you got that sign? I don't understand how you got from this:

At 1 , $2(\pm\frac{1}{\sqrt{2}})=-c$

to this:

$c=2(\mp\frac{1}{\sqrt{2}})$

I have never come across that symbol before. Care to explain what it means please?

And any one have solutions for the other two questions?

$\pm\frac{1}{sqrt{2}}$ means $\frac{1}{sqrt{2}}$ or $-\frac{1}{\sqrt{2}}$

Take for example $x^2=4$

$x=\pm 2$

That means x can be 2 or -2 as well .

Does that clear things up for you ?

**xxravenxx** · October 18th 2009, 11:35 PM

Originally Posted by mathaddict

$\pm\frac{1}{sqrt{2}}$ means $\frac{1}{sqrt{2}}$ or $-\frac{1}{\sqrt{2}}$

Take for example $x^2=4$

$x=\pm 2$

That means x can be 2 or -2 as well .

Does that clear things up for you ?

Yea I know that symbol its just that upside down one that baffles me?

**mathaddict** · October 18th 2009, 11:43 PM

Originally Posted by xxravenxx

Yea I know that symbol its just that upside down one that baffles me?

When you have , $\pm 2$

$-(\pm 2)=\mp 2$

$2 \pm 3 = 5 or -1$

$2\mp 3 = -1 or 5$

**xxravenxx** · October 18th 2009, 11:48 PM

Originally Posted by mathaddict

When you have , $\pm 2$

$-(\pm 2)=\mp 2$

$2 \pm 3 = 5 or -1$

$2\mp 3 = -1 or 5$

Alright. Thanks again.

Any clue on the others? :S

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