If both the roots of `x^2+a x+2=0` lies in the interval (0, 3), then find the exhaustive range of value of `adot`

If both the roots of ax^(2)+ax+1=0 are less than 1, then find the exhaustive range of values of a.

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

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

Let f(x)=0 be a polynomial equation with real coefficients. Then between any two distinct real roots of f(x)=0 , there exists at least one real root of the equation f'(x)=0 . This result is a consequence of the celebrated Rolle's theorem applied to polynomials. Much information can be extracted about the roots of f(x)=0 from the roots of f'(x)=0 . If the three roots of x^(3)-12x+k=0 lie in intervals (-4,-3), (0,1) and (2,3) ,then the exhaustive range of values of k is

If x^(2)-1 =0 then x lies in the interval set

If exactly one root of the quadratic equation x ^(2) -(a+1 ) +2a =0 lies in the interval (0,3) then the set of value 'a' is given by :

If the point P(a ,a^2) lies completely inside the triangle formed by the lines x=0,y=0, and x+y=2, then find the exhaustive range of values of a is (A) (0,1) (B) (1,sqrt2) (C) (sqrt2 -1,1) (D) (sqrt2 -1,2)

If cos^(2)x+sinx+1=0 , then the value of x lies in the interval

If the roots of 3x^(2)- 12x +k = 0 are complex, then find the range of k.