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Quadratic Equations · Class 10 · CBSE Mathematics

Which of the following is a quadratic equation?

Practice question from Quadratic Equations (Class 10 · CBSE Mathematics), with the correct answer and a step-by-step solution.

easy · MCQ · Q-43A16B

Which of the following is a quadratic equation?

  1. A.x2+3x+1=(x−2)2x^2 + 3x + 1 = (x-2)^2Correct answer
  2. B.x(x+1)+8=(x+2)(x−2)x(x + 1) + 8 = (x + 2)(x - 2)
  3. C.x3−4x2−x+1=(x−2)3x^3 - 4x^2 - x + 1 = (x - 2)^3
  4. D.(x+2)3=2x(x2−1)(x + 2)^3 = 2x(x^2 - 1)

Solution

Expanding option A: x2+3x+1=x2−4x+4x^2 + 3x + 1 = x^2 - 4x + 4, which simplifies to 7x−3=07x - 3 = 0 (linear). Expanding option B: x2+x+8=x2−4x^2 + x + 8 = x^2 - 4, which simplifies to x+12=0x + 12 = 0 (linear). Expanding option C: x3−4x2−x+1=x3−6x2+12x−8x^3 - 4x^2 - x + 1 = x^3 - 6x^2 + 12x - 8, which simplifies to 2x2−13x+9=02x^2 - 13x + 9 = 0 (quadratic). Therefore, C is correct.

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