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

• -1 , - 1 + 2ω, - 1 - 2ω²

• -1 , -1, - 1

• -1 , 1 - 2ω, 1 - 2ω²

• -1 , 1 + 2ω, 1 + 2ω²

The quadratic equations x² – 6x + a = 0 and x² – cx + 6 = 0 have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is

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