# Factor theorem maths question

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#1
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
0
1 month ago
#2
(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.
0
1 month ago
#3
(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
0
#4
(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
0
1 month ago
#5
(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?
0
1 month ago
#6
(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 Last edited by boulderingislife; 1 month ago
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#7
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.
1
1 month ago
#8
(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 . Good luck.
0
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