HP -225 Owner's Manual page 164

Since g(x)—h(x)=0, the equation can be rewritten:
f) = g@—hx) = —2x3 + 4x> — 6x + 8 = 0
The value of x for which f(x)=0 is called a root of the equation.
seeks a root for f(x) by evaluating the function repeatedly at
estimates of x, and comparing the results to previous estimates. Using
an complicated algorithm, intelligently chooses a new estimate
where the graph might cross the x-axis.
The graph of the function f(x) = —2x3 + 4x> — 6x + 8 illustrates
that the function has one root. (The example on page 159 calculates
this root.)
f(x)
f(x) = —2x3 + 4x2 — 6x + 8
156 B: More About Solving Equations