SOLUTION: Solve 3x^4 -5x^3-7x^2+3x+2=0 given -1 is a root and 2/3 is a root.

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Question 1134042: Solve 3x^4 -5x^3-7x^2+3x+2=0 given -1 is a root and 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%2B3x%2B2=0+
given: x=-1 is a root and x=2%2F3 is a root
if x=2%2F3=> x-2%2F3=0
if x=-1=>x%2B1=0
x%2B1=0 and x-2%2F3=0 are factor


3x%5E4+-5x%5E3-7x%5E2%2B3x%2B2=0+ is divisible by %28x+%2B+1%29%28x+-2%2F3%29=x%5E2+%2B+x%2F3+-+2%2F3

.....................(3x%5E2-6x-3
x%5E2+%2B+x%2F3+-+2%2F3|3x%5E4+-5x%5E3-7x%5E2%2B3x%2B2+
................................3x%5E4%2Bx%5E3-2x%5E2%2B3x%2B2
.........................................-6x%5E3-2x%5E2
...........................................-6x%5E3-2x%5E2
............................................... +0
3x%5E2-6x-3=0 ...simplify
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%28+4%2B4+%29%29%2F2+

x+=+%282+%2B-+sqrt%28+2%2A4%29%29%2F2+
x+=+%282+%2B-+2sqrt%28+2%29%29%2F2+
x+=+%281+%2B-+sqrt%28+2%29%29+
x=+1%2Bsqrt%282%29 and x=1-sqrt%282%29



+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+3x%5E4+-5x%5E3-7x%5E2%2B3x%2B2%29+