SOLUTION: Solve 3x^4 -5x^3 - 7x^2 + 3x+2 =0 given that 2/3 is a root

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Question 1133830: Solve 3x^4 -5x^3 - 7x^2 + 3x+2 =0 given that 2/3 is a root
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
3x%5E4+-5x%5E3+-+7x%5E2+%2B+3x%2B2+=0+
3x%5E4+-6x%5E3-+3x%5E2-2x%5E3+%2B+4x%5E2%2B2x%2B3x%5E3-6x%5E2-3x-2x%5E2%2B4x%2B2+=0+


%28x+%2B1%29%283x%5E3-6x%5E2-2x%5E2%2B+4x-+3x%2B2%29+=0+
%28x+%2B1%29%28%283x%5E3-2x%5E2%29-%286x%5E2-4x%29-+%283x-2%29%29+=0+
%28x+%2B1%29%28x%5E2%283x-2%29-2x%283x-2%29-+%283x-2%29%29+=0+
%28x+%2B+1%29+%283x+-+2%29+%28x%5E2+-+2x+-+1%29+=+0
roots:
if %28x+%2B+1%29++=+0=>highlight%28x=-1%29
if +%283x+-+2%29++=+0=>3x=2=>highlight%28x=2%2F3%29 (it was given)
if +x%5E2+-+2x+-+1+=+0...use quadratic formula

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%2A1%2A%28-1%29+%29%29%2F%282%2A1%29+
x+=+%282+%2B-+sqrt%284%2B4+%29%29%2F2+
x+=+%282+%2B-+sqrt%282%2A4+%29%29%2F2+
x+=+%282+%2B-+2sqrt%282%29%29%2F2+ ...simplify
x+=+%28cross%282%291+%2B-+cross%282%29sqrt%282%29%29%2Fcross%282%291+
x+=+%281+%2B-+sqrt%282%29%29+

=> solutions:
highlight%28x+=+1+%2B+sqrt%282%29%29+=> approximately 2.4
or highlight%28x+=+1+-+sqrt%282%29+%29=> approximately -0.4


+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+3x%5E4+-5x%5E3+-+7x%5E2+%2B+3x%2B2%29+