GATE AG 2018 • Q12
MCQ • 1 Mark
Section 1: Engineering Mathematics
Numerical Methods
Subtopic: Numerical solutions of ODEs
Question Statement:
Solution of $f(x) = x^4 + 2x^3 - 4x^2 + 3x - 1 = 0$ is:
Options:
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(A) 0.333
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(B) 0.646
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(C) 0.658
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(D) 1.000
Step-by-Step Solution & Explanation
(A) 0.333
(B) 0.646
(C) 0.658
(D) 1.000
Substitute each option and check for f(x) → 0.
x = 0.658: x² = 0.4330, x³ = 0.2849, x⁴ = 0.1875.
f = 0.1875 + 2(0.2849) − 4(0.4330) + 3(0.658) − 1 = 0.1875 + 0.5698 − 1.7320 + 1.9740 − 1 ≈ −0.0007 ≈ 0. ✔
x = 0.646 gives f = −0.018 (not a root); x = 1 gives f = 1 + 2 − 4 + 3 − 1 = 1 ≠ 0; x = 0.333 gives f = −0.396.
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