SOLUTION: Find all real zeros of the function given below. f(x) = x3 - 8x - 3 a. rational zero at x = -3 irrational zeros at x = 5.23 and x = 0.76 b. rational zero at x = 3

Question 43157: Find all real zeros of the function given below.
f(x) = x3 - 8x - 3

a. rational zero at x = -3
irrational zeros at x = 5.23 and x = 0.76
b. rational zero at x = 3
irrational zeros at x = -0.38 and x = -2.62
c. rational zero at x = -3
irrational zeros at x = 2.62 and x = 0.38
d. rational zero at x = 3
irrational zeros at x = -0.76 and x = -5.23
e. None of the others

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
f(x) = x^3 - 8x - 3
f(3)=27-24-3, so 3 is a zero
x-3 is a factor as is x^2+3x+1
The zeroes of this quadratic are:
x=[-3+sqrt(3^2-4)]/2 or x=[-3-sqrt(3^2-4)]/2
x=[-3+sqrt5]/2 or x=[-3-sqrt5]/2
Cheers,
Stan H.

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