alleryIn the polynomial x² + kx + 6, the value of k that makes x − 1 a factor is:
A7
B−5
C5
D−7
Answer & Solution
Correct answer: D. −7
1. By the factor theorem, x − 1 is a factor iff p(1) = 0.
2. p(1) = 1 + k + 6 = k + 7.
3. Setting k + 7 = 0 gives k = −7.
4. Verify: x² − 7x + 6 = (x − 1)(x − 6), confirming x − 1 as a factor.
5. So k = −7.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 9-11 (pp 227-246, 2019 ed.)._
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