MP Board · Class 11 · Mathematics · Complex Numbers and Quadratic EquationsWhat are the roots of the quadratic equation $x^2 + x + 1 = 0$?
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Total Attempts: 3
Accuracy Rate: 33.3%
Step-by-Step Solution
Using the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ for $a=1, b=1, c=1$: $x = \frac{-1 \pm \sqrt{1^2 - 4(1)(1)}}{2(1)} = \frac{-1 \pm \sqrt{-3}}{2} = \frac{-1 \pm i\sqrt{3}}{2}$.
Detailed Options Breakdown
Option : \frac{1 \pm i\sqrt{3}}{2}
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Complex Numbers and Quadratic Equations.
Option 1: \frac{-1 \pm i\sqrt{3}}{2} (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 2: \frac{-1 \pm \sqrt{3}}{2}
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Complex Numbers and Quadratic Equations.
Option 3: 1 \pm i\sqrt{3}
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.