SOLUTION: How do I find all zeros in f(x) = x^3 + 1?

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Question 934640: How do I find all zeros in f(x) = x^3 + 1?
Found 2 solutions by MathLover1, stanbon:
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+x%5E3+%2B+1
set f%28x%29+=0 and use rule: %28a%2Bb%29+%28a%5E2-ab%2Bb%5E2%29; in your case a=x and b=1

0=%28x%2B1%29%28x%5E2-x%2B1%29
solutions:

if 0=%28x%2B1%29=> x=-1-real solution


if 0=%28x%5E2-x%2B1%29-for this one, use quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%2A1%2A1+%29%29%2F%282%2A1%29+

x+=+%281+%2B-+sqrt%28+1-4+%29%29%2F2+
x+=+%281+%2B-+sqrt%28+-3+%29%29%2F2+
x+=+%281+%2B-+i%2Asqrt%28+3+%29%29%2F2+
x+=+%281%2F2+%2B-+i%2Asqrt%28+3+%29%2F2%29+
complex solutions:
x+=+1%2F2+%2B+i%2Asqrt%28+3+%29%2F2+
x+=+1%2F2+-+i%2Asqrt%28+3+%29%2F2+

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E3+%2B+1%29+

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
How do I find all zeros in f(x) = x^3 + 1?
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x^3+1 is divisible by x+1
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x^3+1 = (x+1)(x^2 - x + 1)
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Solve:: (x+1)(x^2-x+1) = 0
If x+1 = 0, x = -1
OR
If x^2-x+1 = 0
x = [1 +- sqrt(1-4*1*1)]/2
x = [1+sqrt(-3)]/2 = (1+isqrt(3))/2
OR
x = (1-isqrt(3)]/2
=================
Cheers,
Stan H.
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