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📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

If a + b + c = 0, one root of ax² + bx + c = 0 is always:

Answer: 1.

  • A 0
  • B 1
  • C -1
  • D 2

Correct answer: B. 1

Explanation: Direct substitution test: put x = 1 into ax²+bx+c: a(1)²+b(1)+c = a+b+c = 0 (given). So x=1 satisfies the equation identically whenever a+b+c=0. Answer: 1 is always a root

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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