anonymous
  • anonymous
When [equation] is divided by (x-1) the remainder is 7. When it is divided by (x+1) the remainder is 3. Determine the values of a &b . Can somebody please just explain the method... thanks:)
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[\huge x^4-4x^3+ax^2+bx+1 \]
anonymous
  • anonymous
Have you tried synthetic division?
anonymous
  • anonymous
but there are 3 variables .. :S

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anonymous
  • anonymous
Yeah but you know a lot of algebra to deal with them.
anonymous
  • anonymous
Hmmm, I'm not exactly sure what the trick for this is.
anonymous
  • anonymous
\[ \large x^4-4x^3+ax^2+bx+1=(x-1)(cx^3+dx^2+ex+f)+7 \]
anonymous
  • anonymous
@ burhan101 use factor and remainder theorem
anonymous
  • anonymous
when f(x) is divided by (x-a) the remainder is given by f(a)
anonymous
  • anonymous
thus here f(x) =x^4−4x^3+ax^2+bx+1 f(1)=7 and f(-1)=3 u will get two equation in two unknowns and u can solev them to know a and b
anonymous
  • anonymous
thus a+b=9 and a-b -3 thus solving above two eq we have a=3 and b=6

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