Find a quadratic polynomial, the sum and product of whose zeroes are $-\dfrac{1}{4}$ and $\dfrac{1}{4}$ respectively.
Step-by-Step Solution
Key Concept: $p(x) = k[x^2 - S x + P] = k[x^2 - (-1/4)x + 1/4] = k[x^2 + x/4 + 1/4]$. For $k=4$, $4x^2 + x + 1$.
$p(x) = k\left(x^2 - \left(-\dfrac{1}{4}\right)x + \dfrac{1}{4}\right) = k\left(x^2 + \dfrac{x}{4} + \dfrac{1}{4}\right)$. [1.0 Mark]
Taking $k = 4$, a required quadratic polynomial is $4x^2 + x + 1$. [1.0 Mark]
---
🎯 Official CBSE Marking Scheme:
Formula substitution: 1.0 Mark
Simplifying with $k=4$ to $4x^2 + x + 1$: 1.0 Mark
Correct Answer: