If both the roots of the quadratic equation x² – 2kx + k² + k – 5 = 0 are less than 5, then k lies in the interval

• (5, 6]

• (6, ∞)

• (-∞, 4)

• [4, 5]

All the values of m for which both roots of the equations x² − 2mx + m² − 1 = 0 are greater than −2 but less than 4, lie in the interval

If the cube roots of unity are 1, ω, ω² then the roots of the equation (x – 1)³ + 8 = 0, are

The value of α for which the sum of the squares of the roots of the equation x² – (a – 2)x – a – 1 = 0 assume the least value is

If roots of the equation x² – bx + c = 0 be two consectutive integers, then b² – 4c equals

If z₁ and z₂ are two non-zero complex numbers such that |z₁ + z₂| = |z₁| + |z2| then argz₁ – argz₂ is equal to