SOLUTION: Find all the zeros of the function using the Rational Root Theorem If f(x) = x^3-4x^2+11x-9 and g(x) = x^2-4x-1 find f(x)-g(x-1) My teacher t

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Find all the zeros of the function using the Rational Root Theorem If f(x) = x^3-4x^2+11x-9 and g(x) = x^2-4x-1 find f(x)-g(x-1) My teacher t      Log On


   

Question 1007663: Find all the zeros of the function using the Rational Root Theorem
If f(x) = x^3-4x^2+11x-9 and g(x) = x^2-4x-1

find f(x)-g(x-1)

My teacher taught how the rational root theorem I'm just confused on when plugging in g(x-1)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

If f%28x%29+=+x%5E3-4x%5E2%2B11x-9 and g%28x%29+=+x%5E2-4x-1

find f%28x%29-g%28x-1%29....since f%28x%29=+x%5E3-4x%5E2%2B11x-9 we need g%28x-1%29=%28x-1%29%5E2-4%28x-1%29-1
then we have:

f%28x%29-g%28x-1%29=+x%5E3-4x%5E2%2B11x-9-%28x%5E2-2x%2B1-4x%2B4-1%29
f%28x%29-g%28x-1%29=+x%5E3-4x%5E2%2B11x-9-%28x%5E2-6x%2B4%29
f%28x%29-g%28x-1%29=+x%5E3-4x%5E2%2B11x-9-x%5E2%2B6x-4
f%28x%29-g%28x-1%29=+x%5E3-5x%5E2%2B17x-13
f%28x%29-g%28x-1%29=+x%5E3-x%5E2-4x%5E2%2B4x%2B13x-13
f%28x%29-g%28x-1%29=+%28x%5E3-x%5E2%29-%284x%5E2-4x%29%2B%2813x-13%29
f%28x%29-g%28x-1%29=+x%5E2%28x-1%29-4x%28x-1%29%2B13%28x-1%29
f%28x%29-g%28x-1%29=%28x-1%29+%28x%5E2-4x%2B13%29
zeros:
%28x-1%29+%28x%5E2-4x%2B13%29=0
if %28x-1%29=0=>highlight%28x=1%29 real zero
%28x%5E2-4x%2B13%29=0...since cannot be factored, use quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-4%29+%2B-+sqrt%28+%28-4%29%5E2-4%2A1%2A13+%29%29%2F%282%2A1%29+
x+=+%284+%2B-+sqrt%28+16-52+%29%29%2F2+
x+=+%284+%2B-+sqrt%28+-36+%29%29%2F2+
x+=+%284+%2B-+6i+%29%2F2+
x+=+%28cross%284%292+%2B-+cross%286%293i+%29%2Fcross%282%29+
x+=+%282+%2B-+3i+%29+
complex zeros:
highlight%28x+=+2+%2B+3i%29++
highlight%28x+=+2+-+3i+%29+