Find the values of k for which distinct roots of `x^(2)+2(k-3)x + 9=0` lie in (-6,1)

Find the least value of k for which the function x^(2) + kx + 1 is an increasing function in the interval 1 lt x lt 2 .

Find the values of k for which the line (k-3) x - (4-k^2) y + k^2 - 7k + 6 = 0 is parallel to the x-axis

Find the values of k for which the line (k-3) x - (4-k^2) y + k^2 - 7k + 6 = 0 is passing through the origin

Determine the value of k for which x+2 is a factor of (x+1)^(7)+(2x+k)^(3)

Find the value of a for which the function (a + 2)x^(3) - 3ax^(2) + 9ax - 1 decreases monotonically for all real x.

Find the values of k for which the line (k-3) x-(4-k^2)y+k^2-7k+6=0 is parallel to the y-axis