If the equation `x^2 +(a-6)x-1=0` is such that there are exactly two integers between the roots of it, then the number of integral values of `a`.

If exactely two integers lie between the roots of equatin x ^(2) +ax-1=0. Then integral value (s) of 'a' is/are :

If the equation sin ^(2) x - k sin x - 3 = 0 has exactly two distinct real roots in [0, pi] , then find the values of k .

Let a,b,c be real numbers such that a+b+c=6 and ab+bc+ca=9, If exactly one root of the equation x^(2)-(m+2)x+5m=0 lies between minimum and maximum value of c , then find the number of integral values of m .

If exactly one root of the equation x^(2)+(k+1)x+5k=0 lies in (0,5) then the number of integral values of k is

Statement-1 : The equation 3x^(5)+15x-18=0 has exactly one real root. Statement-2: Between any two roots of , there is a root of its derivative f'(x) .

Let lal denotes the greatest integer less than or equal to a.Given that the quadratic equation x^(2)+[a^(2)-5a+b+4]x+b=0 has roots -5 and 1, then the number of integral values of a is

if exactly one root of equation x^(2)-(p+1)x-p^(2)=0 lie between 1 and 4 then the number of integral value of p is -

If the equation x ^(4)+kx ^(2) +k=0 has exactly two distinct real roots, then the smallest integral value of |k| is: