Question

Find the value of K for which the quadratic equation (3k+1)x×x+2(k+1)+1=0 has equal roots .. Also find these roots..

Answer 1

$\bold{\boxed{HEY!!!}}$


Here is your answer :-


( 3k + 1 )x² + 2 ( k + 1 ) + 1 = 0


Comparing the equation with standard form


Here


a = 3k + 1


b = 2( k + 1 )


c = 1


Since the given quadratic equation has equal roots the discriminant = 0


b² - 4ac = 0


( 3k + 1 )² - 4 ×2( k + 1 )( 1 ) = 0


=> 9k² + 6k + 1 - 8k - 8 = 0


=> 9k² - 2k - 7 = 0


=> 9k² - 9k + 7k - 7 = 0


=> 9k ( k - 1 ) + 7 ( k - 1 ) = 0


=> ( k - 1 )( 9k + 7 ) = 0


=> k - 1 = 0. or. 9k + 7. = 0


=> k = 1 or. k = -7/9

Answer 2

ʜᴇʀᴇ ɪs ʏᴏᴜʀ ᴀɴsᴡᴇʀ :-


( 3ᴋ + 1 )x² + 2 ( ᴋ + 1 ) + 1 = 0


ᴄᴏᴍᴘᴀʀɪɴɢ ᴛʜᴇ ᴇǫᴜᴀᴛɪᴏɴ ᴡɪᴛʜ sᴛᴀɴᴅᴀʀᴅ ғᴏʀᴍ


ʜᴇʀᴇ


ᴀ = 3ᴋ + 1


ʙ = 2( ᴋ + 1 )


ᴄ = 1


sɪɴᴄᴇ ᴛʜᴇ ɢɪᴠᴇɴ ǫᴜᴀᴅʀᴀᴛɪᴄ ᴇǫᴜᴀᴛɪᴏɴ ʜᴀs ᴇǫᴜᴀʟ ʀᴏᴏᴛs ᴛʜᴇ ᴅɪsᴄʀɪᴍɪɴᴀɴᴛ = 0


ʙ² - 4ᴀᴄ = 0


( 3ᴋ + 1 )² - 4 ×2( ᴋ + 1 )( 1 ) = 0


=> 9ᴋ² + 6ᴋ + 1 - 8ᴋ - 8 = 0


=> 9ᴋ² - 2ᴋ - 7 = 0


=> 9ᴋ² - 9ᴋ + 7ᴋ - 7 = 0


=> 9ᴋ ( ᴋ - 1 ) + 7 ( ᴋ - 1 ) = 0


=> ( ᴋ - 1 )( 9ᴋ + 7 ) = 0


=> ᴋ - 1 = 0. ᴏʀ. 9ᴋ + 7. = 0


=> ᴋ = 1 ᴏʀ. ᴋ = -7/9