Q1. [1] § 4.3 Solution of a Quadratic Equation by Factorisation § 4.5 Summary
The roots of the quadratic equation $(x-1)^2 = 16$ are :
- A $5, 3$
- B $4, -4$
- C $5, -3$
- D $-5, 3$
Previously asked in CBSE board exam
2026 30/3/1 Q1
Generated by claude-sonnet-4-6 · 2026-06-15 10:31 · grounding rag
Model Answer
Option C: 5, −3
$(x-1)^2 = 16 \Rightarrow x-1 = \pm4 \Rightarrow x = 1+4 = 5$ or $x = 1-4 = -3$.
Explanation
Take the square root of both sides to get $x - 1 = \pm 4$, then solve both cases. Many students mistakenly choose B ($4, -4$) by forgetting the "$-1$" shift. Always solve $(x - a)^2 = k$ as $x = a \pm \sqrt{k}$.
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