SOLUTION: How do you find the complex zeroes of the ploynominal function f(x)=x^3+10x?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: How do you find the complex zeroes of the ploynominal function f(x)=x^3+10x?      Log On


   

Question 671880: How do you find the complex zeroes of the ploynominal function f(x)=x^3+10x?
Found 3 solutions by jim_thompson5910, ewatrrr, lwsshak3:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = x^3+10x

0 = x^3+10x

x^3+10x = 0

x(x^2+10) = 0

x = 0 or x^2+10 = 0

x = 0 or x^2 = -10

x = 0 or x = +-sqrt(-10)

x = 0, x = i*sqrt(10) or x = -i*sqrt(10)

So the three solutions are x = 0, x = i*sqrt(10) or x = -i*sqrt(10)

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

f%28x%29=x%5E3%2B10x+=+x%28x%5E2+%2B+10%29 = 0,  IF x^2 + 10 = 0 ⇒ x = ± i%2Asqrt%2810%29 zeroes are  0,i%2Asqrt%2810%29,-i%2Asqrt%2810%29

Note: x^2 = -10 ⇒ x = ± sqrt%2810%28-1%29%29 0r  x = ± sqrt%2810i%5E2%29

Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
How do you find the complex zeroes of the ploynominal function
f(x)=x^3+10x
=x(x^2+10)
x=0
or
x^2+10=0
x^2=-10
x=±√-10
complex zeros: √10 i,-√10 i
note: complex zeroes always come in pairs