The real number `x_1,x_2,x_3` satisfying the equation `x^3-x^2+bx+c=0` are in AP . Find the intervals in which b and c lie.

The real numbers x_(1),x_(2),x_(3) satisfying the equation x^(3)-x^(2)+bx+gamma=0 are in A.P. Find the intervals in which beta and gamma lie.

How many real numbers x satisfy the equation 3^(2x+2)-3^(x+3)-3^(x)+3 = 0 ?

Number of real x satisfying the equation |x -1| = |x - 2| + |x - 3| is

Number of distinct real values of x satisfying the equation x^(3)-5x^(2)+7x-3=0 is

If t is a real number satisfying the equation 2t^(3)-9t^(2)+30-a=0, then find the values of the parameter a for which the equation x+(1)/(x)=t gives six real and distinct values of x .

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

Let x=2 or x=3 satisfy the equation,log_(4)(x^(2)+bx+c)=1. Then find the value of |bc|.

The number of real solutions of the equation 2 sin 3x + sin 7x - 3 = 0 which lie in the interval [-2pi , 2pi] is