The Student Room Group
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>
Competition - post a photo you've taken of nature >>

Factor theorem maths question

Please help with this question I am aware that I need to formulate simultaneous equations this is the stage at which I am currently stuck. I have formulated the 2 simultaneous equations however I am not sure what to do now.

The question: given that (x-1) and (x+1) are factors of px^3 + qx^2 - 3x - 7 find the values of p & q

Any help would be appreciated.
Thanks
Original post by FSan
Please help with this question I am aware that I need to formulate simultaneous equations this is the stage at which I am currently stuck. I have formulated the 2 simultaneous equations however I am not sure what to do now.

The question: given that (x-1) and (x+1) are factors of px^3 + qx^2 - 3x - 7 find the values of p & q

Any help would be appreciated.
Thanks

if x-1 and x+1 are factors, then that means f(1) and f(-1) = 0. You get two simultaneous equations in terms of p and q, and you solve these simultaneously and get p and q. Solving simultaneous equations is gcse stuff so if you've forgotten this, review purple maths website or something to relearn how to solve simultaneous equations.
Reply 2
Avatar for 90 cent
90 cent
16
Original post by boulderingislife
if x-1 and x+1 are factors, then that means f(1) and f(-1) = 0. You get two simultaneous equations in terms of p and q, and you solve these simultaneously and get p and q. Solving simultaneous equations is gcse stuff so if you've forgotten this, review purple maths website or something to relearn how to solve simultaneous equations.

essentially yeah what they've said

plug one value in first so +1
leave that equation even with the unknowns
then plug -1 to the original equation
now you have two simultaneous equations you need to solve for p and q
Reply 3
Avatar for FSan
FSan
OP
14
Original post by 90 cent
essentially yeah what they've said

plug one value in first so +1
leave that equation even with the unknowns
then plug -1 to the original equation
now you have two simultaneous equations you need to solve for p and q


Original post by boulderingislife
if x-1 and x+1 are factors, then that means f(1) and f(-1) = 0. You get two simultaneous equations in terms of p and q, and you solve these simultaneously and get p and q. Solving simultaneous equations is gcse stuff so if you've forgotten this, review purple maths website or something to relearn how to solve simultaneous equations.



Substituting -1 and 1 I get the simultaneous equations:

p + q = 10 and -p - q = 4
Original post by FSan
Substituting -1 and 1 I get the simultaneous equations:

p + q = 10 and -p - q = 4

Can you check the second one?
Original post by FSan
Substituting -1 and 1 I get the simultaneous equations:

p + q = 10 and -p - q = 4

first one is right. minor error in 2nd one. Hint: (-1)^3 = -1, and (-1)^2 = 1 :smile:
(edited 2 years ago)
Reply 6
Avatar for FSan
FSan
OP
14
Oh yes I see now -1^2 is +1 so it would be -p + q = 4 from which o can then proceed. Thank you all for the help.
Original post by FSan
Oh yes I see now -1^2 is +1 so it would be -p + q = 4 from which o can then proceed. Thank you all for the help.

No worries :smile:. Good luck.

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you