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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

Solve 6x² - x - 2 = 0.

Answer: 2/3 and -1/2.

  • A 2/3 and -1/2
  • B 1/2 and -2/3
  • C 1/3 and -2
  • D 2 and -1/3

Correct answer: A. 2/3 and -1/2

Explanation: 6x² - x - 2 = (2x+1)(3x-2) = 0. x = -1/2 or x = 2/3.

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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