SOLUTION: Solve: x^3 +3x^2-14x-20=0

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Question 1134044: Solve: x^3 +3x^2-14x-20=0
Found 2 solutions by Boreal, MathLover1:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
factors can be +/-1,2,4,5,10,20
synthetic division
try 4
4/1---3--- -14---- -20
1 7 14----- doesn't work
-5/1 -2 -4-----20 does work
so (x+5) is a factor and the remainder is from the quotient (x^2-2x-4), which needs the quadratic formula for
x=(1/2)(2+/-sqrt (4+16)) or 1+/- sqrt (5)
the numerical roots are -5,-1.236, 3.236,
graph%28300%2C300%2C-10%2C10%2C-10%2C10%2Cx%5E3%2B3x%5E2-14x-20%29

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E3+%2B3x%5E2-14x-20=0+
x%5E3+-2x%5E2%2B5x%5E2-4x-10x-20=0
%28x%5E3+%2B5x%5E2%29-%282x%5E2%2B10x%29-%284x%2B20%29=0+
x%5E2%28x+%2B5%29-2x%28x%2B5%29-4%28x%2B5%29=0+
%28x+%2B+5%29+%28x%5E2+-+2+x+-+4%29+=+0
solutions:
if %28x+%2B+5%29=+0=>highlight%28x=-5%29
%28x%5E2+-+2+x+-+4%29+=+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%28-4%29+%29%29%2F%282%2A1%29+
x+=+%282+%2B-+sqrt%28+4%2B16+%29%29%2F2+
x+=+%282+%2B-+sqrt%28+20+%29%29%2F2+
x+=+%282+%2B-+sqrt%28+4%2A5+%29%29%2F2+
x+=+%28cross%282%291+%2B-+cross%282%29sqrt%28+5+%29%29%2Fcross%282%291+

x+=+%281+%2B-+sqrt%28+5+%29%29+
solutions: highlight%28x+=+1+%2B+sqrt%28+5+%29%29+ or highlight%28x+=+1+-+sqrt%28+5+%29%29+