Locate roots of `f'(x) = 0`, where `f(x) = (x - a)(x - b)(x -c), a < b < c`

Find number of roots of f(x) where f(x) = 1/(x+1)^3 -3x + sin x

Find number of roots of f(x) where f(x)=(1)/((x+1)^(3))-3x+sin x

Let f(x) be a cubic polynomial with leading coefficient unity such that f(0)=1 and all the roots of f(x)=0 are also roots of f(x)=0. If f(x)dx=g(x)+C, where g(0)=(1)/(4) and C is constant of integration,then g(3)-g(1) is equal to

If f(x) is a cubic polynomial x^3 + ax^2+ bx + c such that f(x)=0 has three distinct integral roots and f(g(x)) = 0 does not have real roots, where g(x) = x^2 + 2x - 5, the minimum value of a + b + c is

If f(x) is a cubic polynomial x^3 + ax^2+ bx + c such that f(x)=0 has three distinct integral roots and f(g(x)) = 0 does not have real roots, where g(x) = x^2 + 2x - 5, the minimum value of a + b + c is

f(x) is a cubic polynomial x^3 + ax^2+ bx + c such that f(x)=0 has three distinct integral roots and f(g(x)) = 0 does not have real roots, where g(x) = x^2 + 2x - 5, the minimum value of a + b + c is

If f(x) is a cubic polynomial x^3 + ax^2+ bx + c such that f(x)=0 has three distinct integral roots and f(g(x)) = 0 does not have real roots, where g(x) = x^2 + 2x - 5, the minimum value of a + b + c is

If f(x) is continuous at x=0 , where f(x)=sin x-cos x , for x!=0 , then f(0)=