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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

If p, q are roots of x² + px + q = 0 (p not= 0), then:

Answer: p = 1, q = -2.

  • A p = 1, q = -2
  • B p = -2, q = 1
  • C p = 1, q = 1
  • D p = q = 0

Correct answer: A. p = 1, q = -2

Explanation: Sum of roots p+q = -p and product pq = q. From product: q(p-1) = 0. Since p not=0, q=0 or p=1. If q=0: p+0=-p, 2p=0, p=0 contradiction. If p=1: 1+q=-1, q=-2. Check product: 1×(-2)=-2=q. Yes, p=1, q=-2.

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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