NCERT · Class 10 · Mathematics · Quadratic EquationsWhat is the nature of the roots of the quadratic equation $2x^2 - 4x + 3 = 0$?
Step-by-Step Solution
For the given quadratic equation $2x^2 - 4x + 3 = 0$: \nComparing with the standard form $ax^2 + bx + c = 0$:
- $a = 2$
- $b = -4$
- $c = 3$ \nThe discriminant ($D$) is given by: $$D = b^2 - 4ac$$ $$D = (-4)^2 - 4(2)(3)$$ $$D = 16 - 24 = -8$$ \nSince $D < 0$, the given quadratic equation has no real roots.
Detailed Options Breakdown
Option : Two distinct real roots
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Quadratic Equations.
Option 1: Two equal real roots
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Quadratic Equations.
Option 2: No real roots (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 3: More than two real roots
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Quadratic Equations.
💡 Study Guide: This question tests core syllabus concepts from Quadratic Equations. For formulas, key summaries, and mock exam reference guides, read the full Quadratic Equations Revision Notes.