If the roots of the equation `2x^(2) + (k + 1) x + (k^(2) - 5k + 6) = 0` are of opposite signes then show that `2 lt k lt 3.`

The value of k for which the equation 3x^(2) + 2x (k^(2) + 1) + k^(2) - 3k + 2 = 0 has roots of opposite signs, lies in the interval

If the roots of the equation x^(2)+8x-(2k+3)=0 differ by 2, then the value of k is

If the roots of the equation 4x^3 -12x^2 +11x +k=0 are in arithmetic progression then k=

If both the roots of the quadratic equation x^(2)-2kx+k^(2)+k-5=0 are less than 5, then k lies in the interval.

Each of the roots of the equation x^(3) - 6x^(2) + 6x - 5 = 0 are increased by k so that the new transformed equation does not contain x^(2) term. Then k =

If the equation (k^(2)-3k +2) x^(2) + ( k^(2) -5k + 4)x + ( k^(2) -6k + 5) =0 is an identity then the value of k is

Let a, b be the roots of the equation x^(2) - 4 x +k_(1) = 0 and c , d the roots of the equation x^(2) - 36 x + k_(2) = 0 If a lt b lt c lt d and a, b,c,d are in G.P. then the product k_(1) k_(2) equals

If one root of the equation (k-1)x^(2) - 10x+ 3 = 0 is the reciprocal of the other, then the value of k is___________ .