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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

If alpha and beta are roots of 2x² + x - 6 = 0, find alpha/beta + beta/alpha.

Answer: 25/24.

  • A 25/24
  • B -25/24
  • C 25/12
  • D -13/12

Correct answer: A. 25/24

Explanation: alpha+beta = -1/2, alpha×beta = -3. alpha/beta + beta/alpha = [(alpha+beta)² - 2 alpha×beta]/(alpha×beta) = [1/4+6]/(-3) = (25/4)/(-3) = -25/12.

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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