Complex Numbers...

The set of values of x for which the inequality [x]² - 5[x] + 6 <  0 (where [.] denote the greatest integral function) hold good is

If the sum of n terms of an A.P. is 2n² + 5n, then find the 4th term.

If the harmonic mean between the roots of (5 + √2)x² - bx + (8 + 2 √5) = 0  is 4, then the value of b is

If α, βare the roots of x² + ax - b = 0 and γ,δare the roots of x² + ax + b = 0 then  (α - γ) (α - δ) (β - δ) (β - γ​) =

If the ratio of the roots of ax² + 2bx + c = 0 is same as the ratio of the roots of px² + 2qx + r = 0 then

The roots of the equation (b - c) x² + 2 (c - a)x +(a - b) = 0 are always

If a ∈Z and the equation (x - a)(x -10) +1 = 0 has integral roots, then values of ‘a ’are

The value of λin order that the equations 2x² + 5 λx + 2 = 0 and 4x² + 8 λx + 3 = 0 have a common root is given by

If both roots of the equation x² - 2ax + a² -1 = 0 lie in the interval (-3,4) then sum of the integral parts of ‘a ’is

Number of rational roots of the equation |x² - 2x - 3| + 4x = 0 is