please find the ans
completing the sq method
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Shubhendu8898:
is there is any condition ?
value ka x or k?
no
then
the gn eq has real and equal roots
we have to find k
ok
tomorrow u ans it's not urgent...
ok..then ..
no problem
Answers
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Hey there!
Given question : 5x² - 4x + 2 + k ( 4x² - 2x - 1 ) = 0 has real and equal roots. Find k.
First, let's sort the coefficients :
5x² - 4x + 2 + 4kx² - 2kx - k
x² ( 5 + 4k ) + x ( -4 - 2k ) + 1 ( 2 - k)
Coefficients :
a = 5 + 4k
b = - ( 4 + 2k )
c = 2 - k
We know that, When the equation has real and equal roots, D = 0
D = b² - 4 ac
0 = [ -( 4 + 2k) ] ² - 4 ( 5 + 4k ) ( 2 - k)
0 = 16 + 4k² + 16k - (20 + 16 k ) ( 2 - k)
0 = 16 + 16k + 4k² - ( 40 - 20k + 32k - 16k² )
0 = 16 + 16k + 4k² - 40 + 20k - 32k + 16k²
0 = k² ( 16 + 4 ) + k ( 16 + 20 - 32 ) + 1 ( 16 - 40 )
0 = 20k² + 4k - 24
4 ( 5k² + k - 6 ) = 0
5k² + k - 6 = 0
5k² + 6k - 5k - 6 = 0
k ( 5k + 6 ) - 1 ( 5k + 6 ) = 0
( 5k + 6 ) ( k - 1 ) = 0
k = -6/5 , 1
Given question : 5x² - 4x + 2 + k ( 4x² - 2x - 1 ) = 0 has real and equal roots. Find k.
First, let's sort the coefficients :
5x² - 4x + 2 + 4kx² - 2kx - k
x² ( 5 + 4k ) + x ( -4 - 2k ) + 1 ( 2 - k)
Coefficients :
a = 5 + 4k
b = - ( 4 + 2k )
c = 2 - k
We know that, When the equation has real and equal roots, D = 0
D = b² - 4 ac
0 = [ -( 4 + 2k) ] ² - 4 ( 5 + 4k ) ( 2 - k)
0 = 16 + 4k² + 16k - (20 + 16 k ) ( 2 - k)
0 = 16 + 16k + 4k² - ( 40 - 20k + 32k - 16k² )
0 = 16 + 16k + 4k² - 40 + 20k - 32k + 16k²
0 = k² ( 16 + 4 ) + k ( 16 + 20 - 32 ) + 1 ( 16 - 40 )
0 = 20k² + 4k - 24
4 ( 5k² + k - 6 ) = 0
5k² + k - 6 = 0
5k² + 6k - 5k - 6 = 0
k ( 5k + 6 ) - 1 ( 5k + 6 ) = 0
( 5k + 6 ) ( k - 1 ) = 0
k = -6/5 , 1
ya
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hey!!both of you don't chat here..on useless topics
i getting distrub
oh! sorry
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