if the equation `x^(2)-x=k-k^(2)` `(k in R)` has one positive and one negative real roots, then number of possible integral values of "k" is

If one root of the equation x^2 - 3kx + (2k -1) = 0 is less than 2 and other root is greater than 4 , then minimum possible integral value of k is

If the equation 4x^(3)+5x+k=0(k in R) has a negative real root then

If exactly one root of the equation x^(2)-2kx+k^(2)-1=0 satisfies the inequality log_(sqrt(3))(2-x)<=0 then find sum of all possible integral values of k

If the equation x^(2) + k^(2) = 2 (k+1)x has equal roots, then what is the value of K?

If the equation x^2 - (2k + 1)x + k + 2 = 0 has exactly one root in (0, 2) such that maximum possible negative integral value of k is m and minimum possible positive integral value of k is M, then IM – m| is

If the equation x^(2)-(2k+1)x+k+2=0 has exactly one root in (0,2) such that maximum possible negative integral value of k is m and minimum possible positive integral value of k is M ,then |M - m| is

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

Consider the quadratic equation (k^(2)-4)x^(2)-(14k+4)x+48=0 has two distinct positive integral roots,then The value of k is

If the equation x^(2)-(2k+1)x+(3k+2)=0 has exactly one root in (-1,4), then the possible interval of the values of k is