# Thread: Sum and Product of roots ><

1. ## Sum and Product of roots ><

Ive got a problem and my maths test is 2mw! gaaaaaa

The roots of the equation X^2 + (P-10)X = 10P are a and a + 4 . Find the possible values of P

a is actually the aplha sign thingy but i dunno how to type it

2. Hello,

You have the equation : X^2 + (P-10)X = 10P

You know that $\alpha$ (click on it to see how i wrote it) and $\alpha+4$ are solutions.

This means that :

$\alpha^2+(P-10) \alpha=10P$
$(\alpha+4)^2+(P-10)(\alpha+4)=10P$

3. I dont get how you derive to this:

$\alpha^2+(P-10) \alpha=10P$
$(\alpha+4)^2+(P-10)(\alpha+4)=10P$

Why is X replaced by $\alpha$

Sorry, but im really dumb at roots. have a phobia of it somehow... Never manage to understand it ><

And thanks for showing me the way to do e alpha thing! ^_^

4. Well, as a and a+4 are solutions, they verify the equation. The equation has x as the unknown, the variable.
So if "a takes the place of x", the equation is true.

The same goes for a+4

5. So does it mean that i dont need to do the aplha + Beta = -b/a way?

6. You can have a go with that

There are multiple ways of solving it, your suggestion is more direct

You may also know alpha*beta

( $\alpha = \alpha \text{ \ and \ } \beta = \alpha + 4$)

7. and how do i do that way then? :P
Im really very confused

8. Well, if you have a trinomial :

ax˛+bx+c=0, $\alpha$ and $\beta$ two roots of the equation, you have :

$\alpha+\beta=\frac{-b}{a}$
and
$\alpha \beta=\frac{c}{a}$

Here, a=1, b=P-10, c=-10P, $\beta=\alpha+4$

And just replace ^^

The system to solve will be :

$\alpha + \alpha +4=\frac{-(P-10)}{1}=10-P$

$\alpha (\alpha+4)=\frac{-10P}{1}=-10P$

The first equation will give : $2 \alpha = 6-P$

Then replace it in the second equation to get P

Sorry, i didn't understand the title as i should have

9. okies...so i got:
$2 \alpha + 4 = 10 - P$ ----- (1)
$\alpha^2 + 4 \alpha = 10P$ -----(2)
from (2) $P = (- \alpha^2 - 4 \alpha )/10$
Is this correct?

10. It's -10P, try to see why :P

(i was editing my post >.<)

11. hahas, i was also editing my post XD
i managed to get the answer now after trying it out

Thanks alot!! ^_^ ^_^

12. So what are the solutions for P ? :-)

13. -6 and -14 ^_^

14. Oh yeaaah

15. Thanks again! =)

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