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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

For the equation 4x² - 12x + 9 = 0, the nature of roots is:

Answer: Two equal real roots.

  • A Two distinct real roots
  • B Two equal real roots
  • C No real roots
  • D One positive one negative

Correct answer: B. Two equal real roots

Explanation: D = 144 - 4(4)(9) = 144 - 144 = 0. Equal roots: x = 12/8 = 3/2.

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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