`(x - 2)(x + 4)-(x - 3)(x - 1) = 0`

Without expanding, find the value of: (i) (x + 1)^4 - 4(x + 1)^3 (x - 1) + 6(x + 1)^2 (x - 1)^2 - 4(x + 1) (x - 1)^3 + (x -1)^4 (ii) (2x - 1)^4 + 4(2x - 1)^3 (3 - 2x) + 6(2x - 1)^2 (3 - 2x)^2 + 4(2x - 1) (3 - 2x)^3 + (3 - 2x)^4

((x + 2) (x ^ (3) -2x + 1)) / (4 + 3x-x ^ (3))> = 0

Let the equation x^(5) + x^(3) + x^(2) + 2 = 0 has roots x_(1), x_(2), x_(3), x_(4) and x_(5), then find the value of (x_(2)^(2) - 1)(x_(3)^(2) - 1)(x_(4)^(2) - 1)(x_(5)^(2) - 1).

Sovle x(x+2)^2(x-1)^5 (2x-3)(x-3)^4 ge 0

Solve x(x+2)^2(x-1)^5 (2x-3)(x-3)^4 ge 0

Sovle x(x+2)^2(x-1)^5 (2x-3)(x-3)^4 ge 0

If |{:(x^(2) +x , 3x - 1 , -x + 3),(2x +1 , 2 + x^(2) , x^(3) - 3),(x - 3, x^(2) + 4, 3x):}| = a_(0) + a_(1) x + a_(2) x^(2) + .... + x_(7) x^(7), then the value of a_(0) is

(x+1)(x-3)(x+2)(x-4)+6=0

The number of roots of equation (((x-1)(x-3))/((x-2)(x-4))-e^(x)) (((x+1)(x+3))/((x+2)(x+4))-e^(-x)) (x^(3)-cos x)=0 :