Let `f(x) = (r-2)(r+1)x^2 + r(r-2)x-r(r-2)=0`, where `r in I, x in R.` If roots of the equation `f(x_i)` are real and `sum_(i=1)^3 (f(x_i))^2 = 0`, then the value of r is

Let r_(1), r_(2) and r_(3) be the solutions of the equation x^(3) - 2 x^(2)+4 x+5074=0 , then the value of (r_(1) +2)(r_(2)+2)(r_(3)+2)

Let r be a root of the equation x^(2)+2x+6=0. The value of (r+2)(r+3)(r+4)(r+5) is

If f(x) = sum_(r=1)^(n)a_(r)|x|^(r) , where a_(i) s are real constants, then f(x) is

Let f: R->R be a function defined by f(x)={[x],(xlt=2) \ \ (0,x >2) where [x] is the greatest integer less than or equal to xdot If I=int_(-1)^2(xf(x^2))/(2+f(x+1))dx , then \ the \ value \ of \ (4I-1)i s

Let r be a root of the equation x^(2)+2x+6=0. The value of (r+2)(r+3)(r+4)(r+5) is equal to-

Let f : R to R be continuous function such that f (x) + f (x+1) = 2, for all x in R. If I _(1) int_(0) ^(8) f (x) dx and I _(2) = int _(-1) ^(3) f (x) dx, then the value of I _(2) +2 I _(2) is equal to "________"

Let R be the set of real number and the mapping f :R to R and g : R to R be defined by f (x)=5-x^(2)and g (x)=3x-4, then the value of (fog) (-1) is

Let R be the set of real number and the mapping f :R to R and g : R to R be defined by f (x)=5-x^(2)and g (x)=3x-4, then the value of (fog) (-1) is

Let F:R to R be such that F for all x in R (2^(1+x)+2^(1-x)), F(x) and (3^(x)+3^(-x)) are in A.P., then the minimum value of F(x) is: