if the equations x2-3x-k=0 and 4x2-11x+2k=0have a common root then find the value of k.also find theb common root?

let c is the common root then c will stisfy both of these equations .

x²-3x-k = 0                 .............1

4x²-11x+2k = 0              ............2

at x = c ,eq 1 becomes

c²-3c-k = 0

2c² - 6c - 2k = 0        ..............3         (after multiplying  by 2)

at x = c, eq 2 becomes

4c²-11c+2k = 0             ................4

adding 3 & 4

6c² -17c = 0

 c = 0 , 17/6

now , put c in any eq 3 or 4

then , k = 0,-17/36

(c,k) = { (0,0) ,(17/6,-17/36) }

this is the required solution ...

approve if u like my ans

Take both as equations

x²-3x-k = 0                 .............1

4x²-11x+2k = 0              ............2

 Solve it by eliminating method:

2x²-6x-2k = 0  [multiply by 2}........(3)

now from eq. (2) and (3)

4x²-11x+2k = 0 

2x²-6x-2k = 0

Solving these equations by eliminating method u will get:

6x²-17x = 0 .....................(4)

x(6x-17) = 0

6x = 17

x = 0, 17/6

Put the value of x in eq...........(4)

k = 0,-17/36

then, 

(c,k) = { (0,0) ,(17/6,-17/36) }