Let `-1lt=plt=1` . Show that the equation `4x^3-3x-p=0` has a unique root in the interval [1/2,1] and identify it.

For -1<=p<=1 , the equation 4x^3-3x-p = 0 has 'n' distinct real roots equation in the interval [1/2,1] and one its root is cos(kcos^-1p) , then the value of n+1/k is :

If both the roots of the equation 4x^(2)-2x+m=0 lie in the interval (-1, 1) , then

Show that the function f(x)=x^(3)+1/(x^(3)) is decreasing function in the interval [-1,1]-{0} .

True or false The equation 2x^2+3x+1=0 has an irrational root.

The equation x log x = 3-x has, in the interval (1,3) :

Given that 2 is a root of the equation 3x^(2)-p(x+1)=0 and that the equation px^(2)-qx+9=0 has equal roots, find the values of p and q.

Statement -1 : one root of the equation x^(2)+5x-7=0 lie in the interval (1,2). and Statement -2 : For a polynomial f(x),if f(p)f(q) lt 0, then there exists at least one real root of f(x) =0 in (p,q)

The roots of the equation 3x^(4)+4x^(3)+x-1=0 consist of

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

The number of solution of x^(3)+4x-1=0 in the interval x in(-2,1) is