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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

Quadratic equation with roots 3 and 5 is:

Answer: x² - 8x + 15 = 0.

  • A x² - 8x + 15 = 0
  • B x² + 8x + 15 = 0
  • C x² - 15x + 8 = 0
  • D x² + 15 = 0

Correct answer: A. x² - 8x + 15 = 0

Explanation: Sum = 8, product = 15. Equation: x² - (sum)x + product = 0, so x² - 8x + 15 = 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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