Let `f(x)=x^(3)+ax^(2)+bx+c` be the given cubic polynomial and `f(x)=0` be the corresponding cubic equation, where `a, b, c in R.` Now, `f'(x)=3x^(2)+2ax+b`
Let `D=4a^(2)-12b=4(a^(2)-3b)` be the discriminant of the equation `f'(x)=0`.
IF `D=4(a^(2)-3b)lt0`. Then,

Let f(x)=x^(3)+ax^(2)+bx+c be the given cubic polynomial and f(x)=0 be the corresponding cubic equation, where a, b, c in R. Now, f'(x)=3x^(2)+2ax+b Let D=4a^(2)-12b=4(a^(2)-3b) be the discriminant of the equation f'(x)=0 . If D=4(a^(2)-3v)=0 , then

Let f(x)=x^(3)+ax^(2)+bx+c be the given cubic polynomial and f(x)=0 be the corresponding cubic equation, where a, b, c in R. Now, f'(x)=3x^(2)+2ax+b Let D=4a^(2)-12b=4(a^(2)-3b) be the discriminant of the equation f'(x)=0 . If D=4(a^(2)-3b)gt0 and f(x_(1)).f(x_(2))gt0 where x_(1),x_(2) are the roots of f'(x), then

Let f(x)=3ax^(2)-4bx+c(a,b,c in R.a!=0) where a,b,c are in A.P.Then the equation f(x)=0 has

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

Let f(x) = ax^(2) - bx + c^(2), b ne 0 and f(x) ne 0 for all x in R . Then

Let f(x)=ax^(5)+bx^(4)+cx^(3)+dx^(2)+ ex , where a,b,c,d,e in R and f(x)=0 has a positive root. alpha . Then,

If b^(2)-4ac=0,a>0 then the domain of the function f(x)=log(ax^(3)+(a+b)x^(2)+(b+c)x+c) is :

Let f(x)=ax^(2)-b|x| , where a and b are constant . Then at x=0 , f(x) has