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)=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))=0" where " x_(1),x_(2) are the roots of f(x) , 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)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)-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)-3b)=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)-3v)=0 , then

Let x^3+ax^2+bx+c be the given cubic polynomlal 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 then 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)=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, a. f(x) has all real roots b. f(x) has one real and two imaginary roots c. f(x) has repeated roots d. None of the above

Let x^3+ax^2+bx+c be the given cubic polynomlal 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 then If D=4a^2-12b=(a^2-3b)lt0. then the roots of the equation f(x) = 0 will be

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