Mathematics · Numerical Analysis
To find a real root of the equation x3 + 4x2 - 10 = 0 in the interval (1, 3/2) by using the fixed-point iteration scheme, consider the following two statements: S1: The iteration scheme xk+1 = √(10 / (4 + xk)), k = 0, 1, 2, ... converges for any initial guess x0 ∈ (1, 3/2) S2: The iteration scheme xk+1 = 1/2 √(10 - xk3), k = 0, 1, 2, ... diverges for some initial guess x0 ∈ (1, 3/2) Then, which one of the following is correct?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1Neither S1 nor S2 is TRUE
- 2Both S1 and S2 are TRUE
- 3S2 is TRUE and S1 is FALSE
- 4S1 is TRUE and S2 is FALSE✓
Correct answer
S1 is TRUE and S2 is FALSE
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