GATE CE 2024 Set 1 — Question 11
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Engineering Mathematics → Numerical Solution of Equations → Nonlinear Algebraic Equations
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Question
The smallest positive root of the equationlies in the range
Correct answer
(A) 0 < x ≤ 2
Solution
The given equation is . We can factorize it by grouping terms:
.
Further factorizing the quadratic in :
.
The roots are . The positive roots are . The smallest positive root is , which lies in the range .
.
Further factorizing the quadratic in :
.
The roots are . The positive roots are . The smallest positive root is , which lies in the range .
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