The GATE Grind

GATE 2026 CE (CE1) – Question 3

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice

At how many points will the curves $y = x^2$ and $y = -x^2 - 2x - 1$ intersect in the real $(x, y)$ plane?

  1. 0
  2. 1
  3. 2
  4. 3

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Show answer and explanation

Correct answer: (A) 0

Explanation

Setting the two equal gives $x^2 = -(x + 1)^2$. The left side is at least 0 and the right side is at most 0, so both would have to be 0, which needs $x = 0$ and $x = -1$ at the same time. That is impossible, so the curves never meet.