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Black Advanced Problems in Mathematics
Exam
Black Advanced Problems in Mathematics
Subject
Mathematics
Chapter
Quadratic Equation

Black Advanced Problems in Mathematics · Mathematics · Quadratic Equation

Which of the following statement(s) is/are correct?

Which of the following statement(s) is/are correct?

Options

  1. AThe number of quadratic equations having real roots which remain unchanged even after squaring their roots is 3.
  2. BThe number of solutions of the equation tan⁡2θ+tan⁡3θ=0\tan 2\theta + \tan 3\theta = 0, in the interval [0,π][0, \pi] is equal to 6.
  3. CFor x1,x2,x3>0x_1, x_2, x_3 > 0, the minimum value of 2x1x2+128x33x22+x224x1x33\frac{2x_1}{x_2} + \frac{128x_3^3}{x_2^2} + \frac{x_2^2}{4x_1x_3^3} equals 24.
  4. DThe locus of the mid-points of chords of the circle x2+y2−2x−6y−1=0x^2 + y^2 - 2x - 6y - 1 = 0, which are passing through origin is x2+y2−x−3y=0x^2 + y^2 - x - 3y = 0.

Correct answer

A. The number of quadratic equations having real roots which remain unchanged even after squaring their roots is 3.

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