alleryWhich of the following second-degree polynomials cannot be factored into first-degree real polynomials?
Ax² − 20x + 91
Bx² + 2x + 2
C4x² − 16x + 15
Dx² + 5x − 84
Answer & Solution
Correct answer: B. x² + 2x + 2
1. A polynomial x² + bx + c factors over the reals iff its discriminant b² − 4c ≥ 0.
2. For x² − 20x + 91: 400 − 364 = 36 > 0, factors.
3. For 4x² − 16x + 15: 256 − 240 = 16 > 0, factors.
4. For x² + 5x − 84: 25 + 336 = 361 > 0, factors.
5. For x² + 2x + 2: 4 − 8 = −4 < 0, no real factors. So x² + 2x + 2 is the one.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 9-11 (pp 227-246, 2019 ed.)._
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