MP Board · Class 9 · Mathematics · PolynomialsIf $x - 1$ is a factor of $p(x) = kx^2 - \sqrt{2}x + 1$, then $k$ equals:
Step-by-Step Solution
Since $(x - 1)$ is a factor of $p(x)$, $p(1) = 0$. $$p(1) = k(1)^2 - \sqrt{2}(1) + 1 = 0$$ $$k - \sqrt{2} + 1 = 0 \implies k = \sqrt{2} - 1$$
Detailed Options Breakdown
Option : $\sqrt{2} + 1$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Polynomials.
Option 1: $\sqrt{2} - 1$ (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 2: $1 - \sqrt{2}$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Polynomials.
Option 3: $-\sqrt{2} - 1$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Polynomials.
💡 Study Guide: This question tests core syllabus concepts from Polynomials. For formulas, key summaries, and mock exam reference guides, read the full Polynomials Revision Notes.