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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

If one root is 3 times the other in x² + px + 12 = 0, find p.

Answer: ±8.

  • A ±4
  • B ±8
  • C ±6
  • D ±5

Correct answer: B. ±8

Explanation: Let roots be a and 3a. Product: 3a² = 12, a = ±2. Sum = 4a = ±8 = -p. p = ±8.

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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