f(x)=2x^3-3x^2-20x+2

Question

estimate the zeros of the given function to the nearest hundreth

Answer 1

We know the shape of the equation of this cubic graph.  If we substitute -20 and + 20 in the equation, we get a large negative value and a large positive value, so the zeros of this cubic must be between these two points.

 

P(-20) = -16798,  P(20) = + 14402

 

So if we try the midpoint we get P(0) = 2.  So there must be some zeros around x = 2.

 

P(5) = 77 and P(-5) = -223, so the zeros must be between these two points.

 

P(.1) = -.028 so there is a zero between x = .1 and x = 0.

 

Continuing to experiment like this we can locate the approximate zeros at 

 

x = .099, x = 3.96, and x = -2.56