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kotesh marikala Grade: 12
        

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?

6 years ago

Answers : (2)

vikas askiitian expert
510 Points
										

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

6 years ago
Vikas TU
6762 Points
										

 


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) }


 


 

6 years ago
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