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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

For what value of k does x² + kx + 9 = 0 have equal roots?

Answer: k = ±6.

  • A k = 3
  • B k = ±6
  • C k = 9
  • D k = ±3

Correct answer: B. k = ±6

Explanation: Equal roots when D = 0: k² - 36 = 0, k² = 36, k = ±6.

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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