MP Board Class 11 Mathematics — If $x = -5 + 2\sqrt{-4}$,

MP Board · Class 11 · Mathematics · Complex Numbers and Quadratic EquationsIf $x = -5 + 2\sqrt{-4}$, find the value of $x^4 + 9x^3 + 35x^2 - x + 4$.

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Total Attempts: 8

Accuracy Rate: 12.5%

Step-by-Step Solution

Here $x = -5 + 4i$. Then $x + 5 = 4i$. Squaring both sides: $(x+5)^2 = 16i^2 \implies x^2 + 10x + 25 = -16 \implies x^2 + 10x + 41 = 0$. Dividing the polynomial $x^4 + 9x^3 + 35x^2 - x + 4$ by $x^2 + 10x + 41$ gives a quotient of $x^2 - x + 4$ and a remainder of 0. Thus, the value is 0.

Detailed Options Breakdown

Option : 0 (Correct Answer)

Correct choice. Refer to the step-by-step verified solution guidelines above for details.

Option 1: 1

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Complex Numbers and Quadratic Equations.

Option 2: -1

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Complex Numbers and Quadratic Equations.

Option 3: 4

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Complex Numbers and Quadratic Equations.

💡 Study Guide: This question tests core syllabus concepts from Complex Numbers and Quadratic Equations. For formulas, key summaries, and mock exam reference guides, read the full Complex Numbers and Quadratic Equations Revision Notes.

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