Q1. [1] § 2.3 Relationship between Zeroes and Coefficients of a Polynomial
If a polynomial $p(x)$ is given by $p(x) = x^2 - 5x + 6$, then the value of $p(1) + p(4)$ is :
- A 0
- B 4
- C 2
- D $-4$
Previously asked in CBSE board exam
2024 30/4/1 Q3
Generated by claude-sonnet-4-6 · 2026-06-15 10:34 · grounding rag
Model Answer
$p(1) = 1 - 5 + 6 = 2$; $p(4) = 16 - 20 + 6 = 2$. So $p(1) + p(4) = 2 + 2 = \mathbf{4}$. Answer: B
Explanation
Substitute x = 1 and x = 4 directly into the polynomial and add the results. Note that 2 and 3 are the zeroes of this polynomial (not 1 or 4), so neither value is zero — students must compute carefully and not guess.
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