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

Find the condition if the equation 3x^(2)+4ax+b=0 has at least one root in (0,1).

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

Let- 1<=p<1 show that the equation 4x^(3)-3x-p=0 has a unique root in the interval [(1)/(2),1]

Rolle's theorem is true for the function f(x)=x^2-4 in the interval

Verify Rolle's theorem for the function f(x) = {log (x^(2) +2) - log 3 } in the interval [-1,1] .

Rolle's theorem is applicable for the function f(x) = |x-1| in [0,2] .

Verify Rolle's therorem for the function f(x) = x (x -1)^(2) in the interval [0,1]

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

Use the Intermediate Value Theorem to show that the polynomial function f(x) = x^(3) + 2x-1 has a zero in the interval [0,1].