anonymous
  • anonymous
when p(x)=x^2 + ax -b is divided by x-1, the remainder is 6. when p(x) is divided by x+2. the remainder is 3. find the values of a and b.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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terenzreignz
  • terenzreignz
Combines polynomials with systems of linear equations. Like I told Faye, the way to get the remainder when f(x) is divided by (x-c) is to simply plug in c into the function. IE Remainder of p(x) when it's divided by x-1... is just p(1) So... what is p(1)
anonymous
  • anonymous
x-c
terenzreignz
  • terenzreignz
wth?

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anonymous
  • anonymous
p(x)=x^2+ax-b
terenzreignz
  • terenzreignz
mhmm so p(1) = ?
anonymous
  • anonymous
i was just asking what x-c is.
terenzreignz
  • terenzreignz
Just an example.
anonymous
  • anonymous
oh. xDD
terenzreignz
  • terenzreignz
Or, a formula. In this case, x-c is x-1
terenzreignz
  • terenzreignz
So, c=1 now just plug in 1 into the function p(x) = x² + ax - b
anonymous
  • anonymous
okaay,, p(1)=(1)^2+a(1)-b
anonymous
  • anonymous
after that??
terenzreignz
  • terenzreignz
Simplify -.- 1² + a(1) - b = 1 + a - b Okay, and this is equal to -6, as per the given. -6 = a - b + 1
anonymous
  • anonymous
sorry,, typo,, its not -6 its only 6
terenzreignz
  • terenzreignz
hmm... 6 = a - b + 1 Understood?
terenzreignz
  • terenzreignz
Or, simplify further, we get a - b = 5
terenzreignz
  • terenzreignz
... stay with me here...
anonymous
  • anonymous
why 6 = a - b + 1??? where did you get +1??
terenzreignz
  • terenzreignz
Focus... since the remainder of p(x) when it's divided by x-1 is 6, it can only mean that p(1) = 6 p(1) = 1² + a(1) - b = 1 + a - b etc
anonymous
  • anonymous
ahah, xDD sorry,, didn't see thatxDD
anonymous
  • anonymous
after that??
terenzreignz
  • terenzreignz
You know a-b = 5 That's not enough to know the value of a and b, you need another equation. Now that we mention it... we have another fact... that when it's divided by x + 2, the remainder is 3. Can only mean that p(-2) = 3 Solve this part.
terenzreignz
  • terenzreignz
Hey... p(-2)... what is it?
anonymous
  • anonymous
huh??
anonymous
  • anonymous
sorry,, we just started doing that today, xDD
terenzreignz
  • terenzreignz
No better time than now. It's just plugging in x = -2... how hard can it be? :P p(-2) = ?
anonymous
  • anonymous
p(-2)=(-2)^2+a(-2)-b
terenzreignz
  • terenzreignz
simplify...
anonymous
  • anonymous
4-2a-b
terenzreignz
  • terenzreignz
And this is equal to...?
anonymous
  • anonymous
2a-b=-4
terenzreignz
  • terenzreignz
Excuse me...?
anonymous
  • anonymous
my eyes hurts,.. T_T
terenzreignz
  • terenzreignz
-.- my eyes *hurt* and anyway... you're losing focus...
anonymous
  • anonymous
-2a-b=4
terenzreignz
  • terenzreignz
Don't you just hate it when the other kid gets the right answer and then 'corrects' it with an incorrect one -.-
terenzreignz
  • terenzreignz
Okay, no more guessing... show your work :P
anonymous
  • anonymous
2a+b=1
terenzreignz
  • terenzreignz
Show your work... let me know you're not guessing...
anonymous
  • anonymous
(-2)^2+a(-2)-b=3 4-2a-b=3 -2a-b=3-4 -2a-b=-1 -2a-b=-1 divide by -1 2a+b=1
terenzreignz
  • terenzreignz
Much better. Now you have both a - b = 5 and 2a + b = 1 I can trust you can solve this system with ease now?
anonymous
  • anonymous
2a+b-1=0
terenzreignz
  • terenzreignz
We certainly have a lot to work on -.- FIRST EQUATION a - b = 5 adding b to both sides gives a = b + 5 Now substitute b+5 for the a in the SECOND equation: 2(b+5) + b = 1 SOLVE FOR b. Get to it...
anonymous
  • anonymous
a=2 b=-3, correct ba toh??
terenzreignz
  • terenzreignz
Nice going, *peanut-butter boy* :P
anonymous
  • anonymous
da eff???? how da eff,,
terenzreignz
  • terenzreignz
pff... Google Derek Bocar... first result... You take so long, I have to find ways to ... kill time... and guess what came up? XD
anonymous
  • anonymous
yeah,, that was really long time agoo, T_T
anonymous
  • anonymous
most humiliating scandal
terenzreignz
  • terenzreignz
mhmm... last bit just killed my appetite :D
terenzreignz
  • terenzreignz
But enough about that. Job well done... you certainly picked this up with more speed than Faye...
anonymous
  • anonymous
i'm really sleeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeepyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy!!!!!!
terenzreignz
  • terenzreignz
Join the club. Why don't you listen to yourself playing? >:)
terenzreignz
  • terenzreignz
LOL Just kidding Peace ^_^
anonymous
  • anonymous
NOOOOOOOOOOOOOOOOOOOOOOOOOOO!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
anonymous
  • anonymous
i'm gonna hack their youtube account!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1
anonymous
  • anonymous
*his
terenzreignz
  • terenzreignz
Come to think of it... just how good are you with that fiddle?
anonymous
  • anonymous
ahm,, xDDD average?? xDDD not really an expert,
terenzreignz
  • terenzreignz
figures... that's no use, I need to hear it. Any excerpts?
anonymous
  • anonymous
i don't really play classical music, so long,,,, xDDD
anonymous
  • anonymous
nope,, i don't really show my skills too much, xDD
terenzreignz
  • terenzreignz
Le gasp... okay, interest over XD time to play some notes on a keyboard... ...the one that looks like a monster's smile and not the one with QWERTY written on it...
terenzreignz
  • terenzreignz
terenzreignz
  • terenzreignz
@derek11111 Listening to myself play is making me even sleepier... you should follow suit. Good night, -peanut butter boy- XD -------------------------------------- Terence out ^_^

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