If `x = 2 - k ` Prove that `x^(3)+6xk+k^(3)-8=0`

If f(x)=[2x]sin3pix then prove that f'(k^(+))=6kpi(-1)^(k) , (where [.] denotes the greatest integer function and k in N).

Find k if x = 3 is a root of equation kx^2 – 10x + 3 = 0

If (x - 3) be a factor of the polynomial (k^(2)x^(3)-kx^(2)+3kx-k) , then find the value of k.

If (x + 1) be a factor of the polynomial p(x)=x^(3)+k , then k =

Find the value of k if (x - 2) is a factor of the polynomial (2x^(5)-6x^(4)-2kx^(3)+6kx^(2)+4kx+8) .

Locus of the image of the point ( 2 ,3) in the line ( 2x - 3y + 4 ) + k ( x - 2y + 3 ) = 0 , k in RR is a _

The asymptotes of the hyperbola x y=h x+k y are (1) x-k=0 and y-h=0 (2)x+h=0 and y+k=0 (3) x-k=0 and y+h=0 (4)x+k=0 and y-h=0

If the equation of the tangent to the circle x^(2) + y^(2) - 2x + 6y - 6 =0 parallel to the line 3x - 4y +7 =0 is 3x - 4y +k=0 , then the value of k is-

If the lines 2x + y - 3 = 0 , 5x + ky - 3 = 0 " and " 3x - y - 2 = 0 are concurrent , find the value of k.

The values of k for which lines kx + 2y + 2 = 0, 2x + ky + 3 = 0, 3x + 3y + k = 0 are concurrent are