The domain of `f(x)=ln(a x^3+(a+b)x^2+(b+c)x+c),` where `a >0, b^2-4ac=0`, is

If the domain of f (x) =1/picos ^(-1)[log _(3) ((x^(2))/(3))] where, x gt 0 is [a,b] and the range of f (x) is [c,d], then :

The domain of the function f(x)=sqrt(x^2-[x]^2) , where [x] is the greatest integer less than or equal to x , is (a) R (b) [0,oo] (c) (-oo,0) (d) none of these

If f(x)=a x^2+b x+c ,g(x)=-a x^2+b x+c ,where ac !=0, then prove that f(x)g(x)=0 has at least two real roots.

Let f(x)=ax^(2)+bx + c , where a in R^(+) and b^(2)-4ac lt 0 . Area bounded by y = f(x) , x-axis and the lines x = 0, x = 1, is equal to :

If f(x)=|(0, x-a, x-b), (x+a, 0, x-c),(x+b, x+c, 0)| , then

Verify Rolle theorem for the function f(x)=log{(x^2+a b)/(x(a+b))}on[a , b], where 0

If f(x) = a + bx + cx^(2) where c > 0 and b^(2) - 4ac < 0 . Then the area enclosed by the coordinate axes,the line x = 2 and the curve y = f(x) is given by

Let f(x)=ln(2+x)-(2x+2)/(x+3) . Statement I The function f(x) =0 has a unique solution in the domain of f(x). Statement II f(x) is continuous in [a, b] and is strictly monotonic in (a, b), then f has a unique root in (a, b).

Let f(x) = a x^2 + bx + c , where a, b, c in R, a!=0 . Suppose |f(x)| leq1, x in [0,1] , then

If the zeros of the polynomial f(x)=a x^3+3b x^2+3c x+d are in A.P., prove that 2b^3-3a b c+a^2d=0 .