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GATE 2026 EE – 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 $x^2=-x^2-2x-1$ gives $2x^2+2x+1=0$. Its discriminant is $4-8=-4<0$, so there are no real solutions: the curves do not intersect.