Ques. if the equation x2-2(k+1)x+(9/2)k=0 has two identical roots then the values of k are:
Answers
Answered by
35
Hi ,
Compare x² - 2(k + 1 )x + 9k/2 = 0
with ax² + bx + c = 0 ,
a = 1 ,
b = - 2( k + 1 ) ,
c = 9k/2 ,
Discreaminant = 0
[ Since equal roots ]
b² - 4ac = 0
[ - 2 ( k + 1 ) ]² - 4 × 1 × 9k/2 = 0
4( k + 1 )² - 18k = 0
2( k + 1 )² - 9k = 0
2 [ k² + 2k + 1 ] - 9k = 0
2k² + 4k + 2 - 9k = 0
2k² - 5k + 2 = 0
2k² - 4k - k + 2 = 0
2k ( k - 2 ) - 1( k - 2 ) = 0
( k - 2 ) ( 2k - 1 ) = 0
Therefore ,
k - 2 = 0 or 2k - 1 = 0
k = 2 or k = 1/2
I hope this helps you.
: )
Compare x² - 2(k + 1 )x + 9k/2 = 0
with ax² + bx + c = 0 ,
a = 1 ,
b = - 2( k + 1 ) ,
c = 9k/2 ,
Discreaminant = 0
[ Since equal roots ]
b² - 4ac = 0
[ - 2 ( k + 1 ) ]² - 4 × 1 × 9k/2 = 0
4( k + 1 )² - 18k = 0
2( k + 1 )² - 9k = 0
2 [ k² + 2k + 1 ] - 9k = 0
2k² + 4k + 2 - 9k = 0
2k² - 5k + 2 = 0
2k² - 4k - k + 2 = 0
2k ( k - 2 ) - 1( k - 2 ) = 0
( k - 2 ) ( 2k - 1 ) = 0
Therefore ,
k - 2 = 0 or 2k - 1 = 0
k = 2 or k = 1/2
I hope this helps you.
: )
Answered by
10
Answer:
❣️ I think it will helps you ❣️
Attachments:
Similar questions