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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

If D = 0, the roots of the quadratic equation are:

Answer: One repeated real root.

  • A Two distinct real roots
  • B One repeated real root
  • C Two imaginary roots
  • D No roots

Correct answer: B. One repeated real root

Explanation: When D = 0, the quadratic has exactly one repeated real root: x = -b/2a.

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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