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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

If 1/alpha and 1/beta are roots of x² + px + q = 0, then alpha, beta are roots of:

Answer: qx² + px + 1 = 0.

  • A x² + px + q = 0
  • B qx² + px + 1 = 0
  • C px² + qx + 1 = 0
  • D x² - px + q = 0

Correct answer: B. qx² + px + 1 = 0

Explanation: Roots are 1/alpha and 1/beta. Sum = 1/alpha + 1/beta = (alpha+beta)/(alpha×beta) = -p/q. Product = 1/(alpha×beta). So equation is x² + (p/q)x + 1/q = 0, or qx² + px + 1 = 0.

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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