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_(1)^(2)-1)(x_(2)^(2) - 1)(x_(3)^(2) - 1)(x_(4)^(2) - 1)(x_(5)^(2) - 1).`

Evaluate lim_(xtooo) ((7x^(2)+1)/(5x^(2)-1))^((x^(5))/(1-x^(3))).

Let x_(1),x_(2), x_(3) be roots of equation x^3 + 3x + 5 = 0 . What is the value of the expression (x_(1) + 1/x_(1))(x_(2)+1/x_(2)) (x_(3)+1/x_(3)) ?

Evaluate lim_(xto0)((1+5x^(2))/(1+3x^(2)))^(1//x^(2))

The equation (|x^2-4x|+3)/(x^2+|x-5|)=1 has

If (2)//(5)(5x)+2(x-1)=4(x+1)-2 , what is the value of x?

If x_(1)+ x_(2)=3, x_(3)+x_(4)=12 and x_(1), x_(2), x_(3), x_(4) are in increasing G.P then the equation having x_(1), x_(2) as roots is

Solve the equation x^4 +4x^3 +5x^2 +2x -2=0 given that -1 + sqrt(-1 ) is a root

The equation x ^(4) -2x ^(3)-3x^2 + 4x -1=0 has four distinct real roots x _(1), x _(2), x _(3), x_(4) such that x _(1) lt x _(2) lt x _(3)lt x _(4) and product of two roots is unity, then : x _(1)x _(2) +x_(1)x_(3) + x_(2) x _(4) +x_(3) x _(4)=

Evaluate: int((x^2+1)(x^2+4))/((x^2+3)(x^2-5))\ dx

Evaluate: int((x^2+1)(x^2+4))/((x^2+3)(x^2-5))\ dx