Prove that the equation `x^(3) + x – 1 = 0` has exactly one real root.

Prove that the equation 3x^(5)+15x-18=0 has exactly one real root.

Prove that the equation x^3 + 2x^2 +x + 4 = 0 has exactly one root in the open interval (-3,-2).

Prove that the equation,3x^(3)-6x^(2)+6x+sin x=0 has exactly one real root.

Prove that the equation 3x^(5)+15x -8=0 has only one real root .

Prove that the equation x^(4)-4x -1 =0 has two different real roots .

Statement-1 : The equation 3x^(5)+15x-18=0 has exactly one real root. Statement-2: Between any two roots of , there is a root of its derivative f'(x) .

Prove that the equation Z^(3)+iZ-1=0 has no real roots.

Thus f(0)=f(1) and hence equation f\'(x)=0 has at least one root between 0 and 1. Show that equation (x-1)^5+(2x+1)^9+(x+1)^21=0 has exactly one real root.

Thus f(0)=f(1) and hence equation f\'(x)=0 has at least one root between 0 and 1. Show that equation (x-1)^5+(2x+1)^9+(x+1)^21=0 has exactly one real root.

For which values of 'a' so that the equation x^(2)+(3-2a)x+a=0 has exactly one root in the interval (-1,2)