CBSE · Class 10 · Mathematics · Quadratic EquationsFor what value of $k$ does the quadratic equation $x^2 - kx + 9 = 0$ have equal real roots?
Step-by-Step Solution
The given quadratic equation is $x^2 - kx + 9 = 0$. \nComparing with $ax^2 + bx + c = 0$, we have: $a = 1, b = -k, c = 9$ \nFor equal real roots, the discriminant must be zero ($D = 0$): $D = b^2 - 4ac = 0$ $(-k)^2 - 4(1)(9) = 0$ $k^2 - 36 = 0$ $k^2 = 36$ $k = \pm 6$ \nTherefore, the correct option is (B).
Detailed Options Breakdown
Option : ± 3
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Quadratic Equations.
Option 1: ± 6 (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 2: ± 9
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Quadratic Equations.
Option 3: 6 only
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.