At what values of a do all the zeroes of the function `f(x)=(a-2)x^2+2ax+a+3` lies on the interval (-2,1)

Find all the values of 'a' for which both the roots of the equation (a-2)x^(2)-2ax+a=0 lies in the interval (-2,1).

Find all the values of 'a' for which both the roots of the equation (a - 2)x^2 - 2ax + a = 0 lies in the interval (-2,1) .

the value of the function f(x)=(x^(2)-3x+2)/(x^(2)+x-6) lies in the interval.

What are the values of c for which Rolle's theorem for the function f(x)=x^(3)-3x^(2)+2x in the interval [0,2] is verified?

For what values of a do the graphs of the functions y=2ax+1 and y=(a-6)x^(2)-2 not intersect?

The value of a for which all extremum of function f(x)=x^(3)+3ax^(2)+3(a^(2)-1)x+1 , lie in the interval (2, 4) is

The value of a for which all extremum of function f(x)=x^(3)+3ax^(2)+3(a^(2)-1)x+1 , lie in the interval (2, 4) is

The value of a for which all extremum of function f(x)=x^(3)+3ax^(2)+3(a^(2)-1)x+1 , lie in the interval (-2, 4) is

The mean value of the function f(x) = (1)/( x^2 + x) on the interval [1, 3//2] is