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10 cards from this deck
Conditions like repeated roots or discontinuities cause failure.
No sign change detected as function touches xxx-axis.
f(x)=(x−2)2f(x) = (x - 2)^2f(x)=(x−2)2 has a root at x=2x = 2x=2 without a sign change.
They may jump over roots, neglecting sign changes.
Newton-Raphson and fixed-point iteration may be more effective.
f(x)=1/xf(x) = 1/xf(x)=1/x is undefined at x=0x = 0x=0, showing discontinuity.
No sign change detected even though roots exist in interval.
f(a)f(a)f(a) and f(b)f(b)f(b) both positive or both negative show no change.
It relies on continuity within the interval to detect roots.
Discontinuities prevent detection of root sign changes.
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