Find the value of k that the following quadratic equation has equal roots. (K-12)x2-2(k-12)x+2=0
Answers
Answered by
12
Given :
( k - 12 )x² - 2 ( k - 12 )x + 2 = 0
Comparing with a x² + b x + c = 0 we get :-
a = k - 12
b = - 2 ( k - 12 )
c = 2
The equation has equal roots !
So b² = 4 a c
==> ( - 2 ( k - 12 ) )² = 2 ( k - 12 )
==> ( - 2 )² ( k - 12 )² = 2 ( k - 12 )
==> 2 ( k² + 144 - 24 k ) = k - 12
==> 2 k² + 288 - 48 k = k - 12
==> 2 k² - 49 k + 300 = 0
==> 2 k² - 25 k - 24 k + 300 = 0
==> k ( 2 k - 25 ) - 12 ( 2 k - 25 ) = 0
==> ( 2 k - 25 )( k - 12 ) = 0
Either :
k - 12 = 0
==> k = 12
or :
2 k - 25 = 0
==> 2 k = 25
==> k = 25/2 = 12.5
The value of k is 12 or 12.5
Hope it helps : )
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manushi23:
I got the roots as 12 and 14
and the answer key says its 12 and 20 and I dont know how
my answer is correct so long if there is no error in the logic . see if u find any error otherwise it is correct . sometimes it happens that book's answers are wrong
Answered by
5
a = k - 12
b = - 2 ( k - 12 )
c = 2
The equation has equal roots !
So b² = 4 a c
=> ( - 2 ( k - 12 ) )² = 2 ( k - 12 )
=> ( - 2 )² ( k - 12 )² = 2 ( k - 12 )
=> 2 ( k² + 144 - 24 k ) = k - 12
=> 2 k² + 288 - 48 k = k - 12
=> 2 k² - 49 k + 300 = 0
=> 2 k² - 25 k - 24 k + 300 = 0
=> k ( 2 k - 25 ) - 12 ( 2 k - 25 ) = 0
=> ( 2 k - 25 )( k - 12 ) = 0
Either :
k - 12 = 0
=> k = 12
or :
2 k - 25 = 0
=> 2 k = 25
=> k = 25/2 = 12.5
The value of k is 12 or 12.5
hope u understand ❤️❤️
b = - 2 ( k - 12 )
c = 2
The equation has equal roots !
So b² = 4 a c
=> ( - 2 ( k - 12 ) )² = 2 ( k - 12 )
=> ( - 2 )² ( k - 12 )² = 2 ( k - 12 )
=> 2 ( k² + 144 - 24 k ) = k - 12
=> 2 k² + 288 - 48 k = k - 12
=> 2 k² - 49 k + 300 = 0
=> 2 k² - 25 k - 24 k + 300 = 0
=> k ( 2 k - 25 ) - 12 ( 2 k - 25 ) = 0
=> ( 2 k - 25 )( k - 12 ) = 0
Either :
k - 12 = 0
=> k = 12
or :
2 k - 25 = 0
=> 2 k = 25
=> k = 25/2 = 12.5
The value of k is 12 or 12.5
hope u understand ❤️❤️
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