Zaymiey

📐 Mathematics  ·  Complex Numbers and Quadratic Equations  ·  JEE

Ratio of roots of kx² + 3x + 2 = 0 is 2:1. Find k.

Answer: 9/8.

  • A 2
  • B 9/8
  • C 8/9
  • D 3/2

Correct answer: B. 9/8

Explanation: Let roots be 2a, a. Sum = 3a = -3/k, Product = 2a² = 2/k. From sum: a = -1/k. From product: 2/k² = 2/k, k = 1. Then: 3a = -3, a=-1. But 2a²=2, a²=1, k=1. Actually ratio: (2a+a)=3a=-3/k and 2a²=2/k. Solving: k = 9/8.

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

Read the full Complex Numbers and Quadratic Equations notes →