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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

The product of all real roots of x² - |x| - 6 = 0 is:

Answer: -9.

  • A -6
  • B 6
  • C 9
  • D -9

Correct answer: D. -9

Explanation: Let t = |x| (t ≥ 0). The equation becomes t²−t−6 = 0, factoring as (t−3)(t+2) = 0. Only t = 3 is non-negative, so |x| = 3, giving x = 3 or x = −3. Product of all real roots = 3 × (−3) = −9.

Argand Plane: z = a + ibReImz = a+iba (real part)b (imaginary part)θ = arg(z)|z| = length of the vector OZ = √(a²+b²); θ = angle OZ makes with the positive real axis

A complex number z = a+ib is plotted as a point (or vector from the origin) on the Argand plane, with the real part along the horizontal axis and the imaginary part along the vertical; its modulus |z| is the vector's length, and its argument θ is the angle from the positive real axis.

Concept context

Complex numbers in a+ib form, modulus, argument, polar form, cube roots of unity, and quadratic equations with complex roots

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