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Mathematics — CBSE Class 10 board question

Q1. [1]
Zeroes of the polynomial $p(x) = x^2 - 3x + 4$ are:
  1. A $-2, \; -2$
  2. B $2, \; -2$
  3. C $-4, \; -3$
  4. D $3, \; 2$
Previously asked in CBSE board exam
2025 30/3/1 Q17
Generated by claude-sonnet-4-6 · 2026-06-15 10:34 · grounding rag
Model Answer

Option D is incorrect. The discriminant of $x^2 - 3x + 4$ is $b^2 - 4ac = 9 - 16 = -7 < 0$, so this polynomial has no real zeroes. None of the given options is correct.

(If forced to choose from the options as given, none is correct.)

Source: Chapter 2, Section 2.3

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Explanation

The discriminant $D = b^2 - 4ac = (-3)^2 - 4(1)(4) = 9 - 16 = -7 < 0$ means the parabola does not intersect the x-axis, so there are no real zeroes (Case iii from Section 2.2). This is a trick/error question — examiners sometimes test whether students blindly match options or actually verify. If this appears on a real paper, write the discriminant calculation and state no real zeroes exist. Check options by substituting: none of the pairs satisfies the polynomial.

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