Let `-1leple1`, show that the equation `4x^(3)-3x-p=0` has a unique root in the interval `[1/2,1]` and identify it.

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.

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

If the equation x^(3) - 3x + a = 0 has distinct roots between 0 and 1, then the value of a is

If the equation x^(3)-6x^(2)+9x+lambda=0 has exactly one root in (1, 3), then lambda belongs to the interval

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.