Find all real zeros of the function
f(x)=x^3-27x
0=x^3 - 27x
You can factor out an x on right hand side
0= x(x^2-27)
X=0
X=-sqrt(27)
X=sqrt(27)
To find the real zeros of the function f(x) = x^3 - 27x, we need to set the function equal to zero and solve for x.
Step 1: Set the function equal to zero: f(x) = x^3 - 27x = 0.
Step 2: Factor out x: x(x^2 - 27) = 0.
Step 3: Set each factor equal to zero and solve for x:
a) x = 0
b) x^2 - 27 = 0
For the second equation, we can solve for x^2 by adding 27 to both sides:
x^2 = 27.
Now, we can take the square root of both sides to solve for x:
x = ±√27.
Simplifying the square root of 27, we get x = ±√(3^3) = ±3√3.
So, the real zeros of the function f(x) = x^3 - 27x are x = 0, x = -3√3, and x = 3√3.