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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

Number of real solutions of 4x² - 5×2<sup>x+1</sup> + 4 = 0:

Answer: 2.

  • A 0
  • B 1
  • C 2
  • D 3

Correct answer: C. 2

Explanation: Let t = 2<sup>x</sup> (t>0). 4t² - 10t + 4 = 0. 2t² - 5t + 2 = 0. (2t-1)(t-2) = 0. t = 1/2 or t = 2. x = -1 or x = 1. Two real solutions.

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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