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Find the value of 2x4 + 5x3 + 7x2 – x + 41, when x = i-2-3i. - Mathematics

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Question

Find the value of 2x4 + 5x3 + 7x2 – x + 41, when x = `-2 - sqrt(3)"i"`.

Sum
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Solution

x + 2 = `- sqrt(3)"i"` ⇒ x2 + 4x + 7 = 0

Therefore, 2x4 + 5x3 + 7x2 – x + 41

= (x2 + 4x + 7)(2x2 – 3x + 5) + 6

= 0 × (2x2 – 3x + 5) + 6

= 6

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Chapter 5: Complex Numbers and Quadratic Equations - Solved Examples [Page 81]

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NCERT Exemplar Mathematics [English] Class 11
Chapter 5 Complex Numbers and Quadratic Equations
Solved Examples | Q 11 | Page 81

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