Question

Find the value(s) of ‘m’ for which the following
equation has equal roots: [3]
(m – 12)x
2
+ 2(m – 12)x + 2 = 0

Answer 1

Answer:

Discriminant must be 0 for equal roots:

Here,

If Discriminant is 0

→ [ 2( m - 12 )]² - 4( m - 12 )( 2 ) = 0

→ 4( m - 12 )² - 4( m - 12 )(2) = 0

→ ( m - 12 )² - 2( m - 12 ) = 0

→ ( m - 12 )( m - 12 - 2 ) = 0

→ ( m - 12 ) ( m - 14 ) = 0

→ m - 12 = 0 or m - 14 = 0

→ m = 12 or 14