9. Find the value of m for which the equation(m + 4)/2 + (m + 1)x + 1 = 0 has real andequal roots. About the author Skylar
[tex]\boxed{\boxed{\bf{\green{answer = > }}}} [/tex] The roots of the equation are equal . The given equation is ( 4 + m ) x² + ( m + 1 ) x + 1 = 0 . Comparing with a x² + bx + c = 0 : a = 4 + m b = m + 1 c = 1 When the roots of the equation are equal , then we can write that b² = 4 ac . Hence : ( m + 1 )² = 4 ( 4 + m ) 1 ⇒ m² + 1 + 2 m = 16 + 4 m ⇒ m² – 2 m – 15 = 0 Splitting – 2m into 3 m – 5 m we get :- ⇒ m² + 3 m – 5 m – 15 = 0 Take commons :- ⇒ m ( m + 3 ) – 5 ( m + 3 ) = 0 ⇒ ( m – 5 )( m + 3 ) = 0 Either, m = 5 . Or, m = – 3 [tex]\boxed{\boxed{\bf{\red{Either\:m=5\:or\:m=-3}}}} [/tex] Step-by-step explanation:- It is not mentioned in the question . The roots of the equation will be equal . When roots are equal : b² = 4 ac When roots are unequal and real :- b² > 4 ac When roots are complex : b² < 4 ac Apply the above formula and then find the value of m 🙂 . Reply
[tex]\boxed{\boxed{\bf{\green{answer = > }}}} [/tex]
The roots of the equation are equal .
The given equation is ( 4 + m ) x² + ( m + 1 ) x + 1 = 0 .
Comparing with a x² + bx + c = 0 :
When the roots of the equation are equal , then we can write that b² = 4 ac .
Hence :
( m + 1 )² = 4 ( 4 + m ) 1
⇒ m² + 1 + 2 m = 16 + 4 m
⇒ m² – 2 m – 15 = 0
Splitting – 2m into 3 m – 5 m we get :-
⇒ m² + 3 m – 5 m – 15 = 0
Take commons :-
⇒ m ( m + 3 ) – 5 ( m + 3 ) = 0
⇒ ( m – 5 )( m + 3 ) = 0
Either,
Or,
[tex]\boxed{\boxed{\bf{\red{Either\:m=5\:or\:m=-3}}}} [/tex]
Step-by-step explanation:-
It is not mentioned in the question .
The roots of the equation will be equal .
When roots are equal :
b² = 4 ac
When roots are unequal and real :-
b² > 4 ac
When roots are complex :
b² < 4 ac
Apply the above formula and then find the value of m 🙂 .
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