SOLUTION: find the roots of the equation by any convenient method. show your work. 1. x^3-6x^2+4x=0 2. x^4-5x^2+4=0 3. 3x^3+12x^2-x-4=0 4. (3x+5)(x^2+5x-6) can you show the work be

Algebra ->  Rational-functions -> SOLUTION: find the roots of the equation by any convenient method. show your work. 1. x^3-6x^2+4x=0 2. x^4-5x^2+4=0 3. 3x^3+12x^2-x-4=0 4. (3x+5)(x^2+5x-6) can you show the work be      Log On


   

Question 926612: find the roots of the equation by any convenient method. show your work.
1. x^3-6x^2+4x=0
2. x^4-5x^2+4=0
3. 3x^3+12x^2-x-4=0
4. (3x+5)(x^2+5x-6)
can you show the work because i keep getting the wrong answers
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
1.
x%5E3-6x%5E2%2B4x=0 factor out x
x%28x%5E2-6x%2B4%29=0 => one solution is x=0
x%5E2-6x%2B4=0 use quadratic formula to find other two solutions:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-6%29+%2B-+sqrt%28+%28-6%29%5E2-4%2A1%2A4+%29%29%2F%282%2A1%29+
x+=+%286+%2B-+sqrt%2836-16%29%29%2F2+
x+=+%286+%2B-+sqrt%2820%29%29%2F2+
x+=+%286+%2B-+sqrt%284%2A5%29%29%2F2+
x+=+%28cross%286%293+%2B-+cross%282%29sqrt%285%29%29%2Fcross%282%29+
x+=+%283+%2B-+sqrt%285%29%29+
solutions:
highlight%28x+=+3+%2B+sqrt%285%29%29+
highlight%28x+=+3+-+sqrt%285%29%29+

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E3-6x%5E2%2B4x%29+



2.
x%5E4-5x%5E2%2B4=0....factor completely
x%5E4-x%5E2-4x%5E2%2B4=0
%28x%5E4-x%5E2%29-%284x%5E2-4%29=0
x%5E2%28x%5E2-1%29-4%28x%5E2-1%29=0
%28x%5E2-4%29%28x%5E2-1%29=0
%28x-2%29%28x%2B2%29%28x-1%29%28x%2B1%29=0
solutions:
if %28x-2%29=0=>highlight%28x=2%29
if %28x%2B2%29=0=>highlight%28x=-2%29
if %28x-1%29=0=>highlight%28x=1%29
if %28x%2B1%29=0=>highlight%28x=-1%29



3.
3x%5E3%2B12x%5E2-x-4=0
3x%5E2%28x%2B4%29-%28x%2B4%29=0
%283x%5E2-1%29%28x%2B4%29=0

solutions:
if %283x%5E2-1%29=0=>3x%5E2=1=>x%5E2=1%2F3=>x=sqrt%281%2F3%29=>highlight%28x=1%2Fsqrt%283%29%29 or x=highlight%28-1%2Fsqrt%283%29%29
if %28x%2B4%29=0=>highlight%28x=-4%29
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C%283x%5E2-1%29%28x%2B4%29%29+


4.
%283x%2B5%29%28x%5E2%2B5x-6%29=0+
%283x%2B5%29%28x%5E2-x%2B6x-6%29=0+
%283x%2B5%29%28%28x%5E2-x%29%2B%286x-6%29%29=0+
%283x%2B5%29%28x%28x-1%29%2B6%28x-1%29%29=0+
%283x%2B5%29%28x%2B6%29%28x-1%29=0+

solutions:
if %283x%2B5%29=0+=>3x=-5=>highlight%28x=-5%2F3%29
if %28x%2B6%29=0+=> highlight%28x=-6%29
if %28x-1%29=0+=>highlight%28x=1%29

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C%283x%2B5%29%28x%2B6%29%28x-1%29%29+