SOLUTION: find all solution ( real and complex) to the equation: x^4+3x^2=x^3 find all zeros of the function: f(x)= 2x^3+10x

Algebra ->  Linear-equations -> SOLUTION: find all solution ( real and complex) to the equation: x^4+3x^2=x^3 find all zeros of the function: f(x)= 2x^3+10x      Log On


   

Question 365840: find all solution ( real and complex) to the equation: x^4+3x^2=x^3

find all zeros of the function: f(x)= 2x^3+10x
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E4%2B3x%5E2=x%5E3
x%5E4-x%5E3%2B3x%5E2=0
x%5E2%28x%5E2-x%2B3%29=0
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highlight%28x=0%29 is the real solution.
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x+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%2A1%2A3+%29%29%2F%282%2A1%29+
x+=+%281+%2B-+sqrt%28+1-12%29%29%2F%282%29+
x+=+%281+%2B-+sqrt%28+-11+%29%29%2F%282%29+
highlight%28x+=+%281+%2B-+sqrt%2811%29i%29%2F2%29+ is the complex solution.
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f%28x%29=+2x%5E3%2B10x=0
2x%28x%5E2%2B5%29=0
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highlight_green%28x=0%29
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x%5E2%2B5=0
x%5E2=-5
highlight_green%28x=0+%2B-+sqrt%285%29i%29