If $4$ is a zero of the polynomial $p(x) = x^2 - x - (2 + 2k)$, then the value of $k$ is :

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Accepted Answer

## Model Answer **(A) 3** Since 4 is a zero, $p(4) = 0$: $4^2 - 4 - (2 + 2k) = 0 \Rightarrow 16 - 4 - 2 - 2k = 0 \Rightarrow 10 = 2k \Rightarrow k = 3$. ## Explanation Substitute x = 4 into p(x) and set it equal to zero (definition of a zero). Solve the resulting linear equation for k. The key concept is: k is a zero of p(x) if p(k) = 0 (Chapter 2, Section 2.1).

Mathematics — CBSE Class 10 board question