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 Rolles theorem,prove that there is at least one root in (45(1)/(10),46) of the equation.P(x)=51x^(101)-2323(x)^(100)-45x+1035=0

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

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

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

The number of terms in (1+x)^(101)(1+x^(2)-x)^(100) is:

Find the roots of the equation 100x^2-20x+1

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

IF alpha be a root of the equation 3x^2-4x+5=0 , prove that 2alpha^2 is a root of the equation 9x^2+28x+100=0 .

Using the Rolle theorem prove that the derivative f.(x) of the function. {:f(x)={:{(x sinpix,"at",xgt0),(0,"at",x=0):} vanishes on an infinite set of points of the interval (0,1).