CBSE · Class 10 · Mathematics · PolynomialsIf one zero of the polynomial $p(x) = (k^2 + 4)x^2 + 13x + 4k$ is the reciprocal of the other, then $k$ is equal to:
Step-by-Step Solution
Let one zero be $\alpha$, then the other is $\frac{1}{\alpha}$.\nProduct of zeroes = $\alpha \times \frac{1}{\alpha} = 1$.\nAlso, product of zeroes is given by $\frac{c}{a} = \frac{4k}{k^2 + 4}$.\nTherefore, $\frac{4k}{k^2 + 4} = 1 \implies 4k = k^2 + 4 \implies k^2 - 4k + 4 = 0 \implies (k - 2)^2 = 0 \implies k = 2$.
Detailed Options Breakdown
Option : 2 (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 1: -2
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Polynomials.
Option 2: 4
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Polynomials.
Option 3: -4
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.