Complex Numbers...

The set of real values of x satisfying  |x-1| < 3 and |x - 1| > 1

Let f(x) be a polynomial for which the remainders when divided by x –1, x –2, x –3 respectively 3, 7, 13. Then the remainder of f(x) when divided by (x –1) (x –2) (x –3) is

The range of values of x which satisfy 5x + 2 <3x + 8 and  

For x ∈R, the least value of  

Suppose a² = 5a –8 and b² = 5b –8, then equation whose roots are a/b and b/a is

If α,βare roots of ax² + bx + c = 0, then roots of a³ x² + abcx + c³ = 0 are  

If P(x) = ax² + bx + c and Q(x) = -ax² + dx + c, where ac ≠0, then P(x)Q(x) = 0 has  

If the product of the roots of the equation x² –5kx + 2e^{4 ln k} - 1 = 0 is 31, then sum of the root is  

Let α, βbe the roots of the equation x²  - px + r = 0 and (α/2), 2 βbe the roots of the equation x²  - qx + r = 0. Then the value of r is  

The sum of all the real roots of the equation |x –2|² + |x –2| –2 = 0 is