If k satisfies `k^2 - k-6 > 0,` then a value exists for

If the matrix A=({:(0,2),(K,-1):}) satisfies A(A^(3)+3I)=2I , then then value of K is

If x=3 and y=-2 satisfy 2x-3y=k , then find the value of k .

If a^2-a-6=(a+2)(a-k) ,the value of k is

If x^(2) + kx + 3k = 0 has no solution , then the value of k will satisfy

If x^2 + kx + k= 0 has repeated roots, then the value of k will satisfy:

If (alpha+5i)/(2) is a root of the equation 2x^(2)-6x+k=0 ,then the value of k/10 is alpha, k, in R)

If k be positive integer , then the number of values of k satisfying int_0^(pi/2)[k^2(cos3x+1/2cosx)+sinx-2kcosx]dxlt=1 is

If k be positive integer,then the number of values of k satisfying int_(0)^((pi)/(2))[k^(2)(cos3x+(1)/(2)cos x)+sin x-2k cos x]dx<=1

For what values of k is the inequality x^(2)-(k-3)x-k+6>0 valid for all real x?