Using Rolles theorem, prove that there is at least one root in `(45^(1/(100)),46)` of the equation. `P(x)=51 x^(101)-2323(x)^(100)-45 x+1035=0.`

Using Rolle's theorem prove that the equation 3x^(2)+px-1=0 has the least one it's interval (-1,1) .

The equation sin x+x cos x=0 has at least one root in

Using Rolle's theorem, find the point on the curve y = x(x -4), x in [0, 4]

Solve the equation x^(2)-45x+324=0 .

Product of roots of equation x^(log_(10)x)=100x is

Using Rolle's theorem prove that there exista point between ]1,0[ and ]3,0[ on the curve f(x)=x^(2)-4x+3 at which the tangent is parallel to x-axis.

Prove that the equation x 2^x= 1 has at least one positive root which is less than unity.

prove that the roll's theorem is not applicable for the function f(x)=2+(x-1)^((2)/(3)) in [0,2]

The sum of the reciprocals of the roots of the equation (101)/(123)x+(1)/(x)+1=0