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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?

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?

Grade:12

3 Answers

vikas askiitian expert
509 Points
13 years ago

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

Vikas TU
14149 Points
13 years ago

 

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) }

 

 

Vishruti
19 Points
6 years ago
x2 -4x+k = 0 and x2+kx-4 =0 have a common root, so let’s take it y
putting value of y
y2-4y+k=0 ----{1}
y2-ky+4=0 ------{2}
substracting {1} from {2}
y2-4y+k-[ y2-ky+4]
y2-4y+k-y2+ky-4=0
-y(k+4)+4+k=0
4+k= y(k+4)
y=1
putting y=1 in eq {1}
y2-4y+k=0
(1)2-4(1)+k=0
1-4+k=0
k=3

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