Question

9. Find the value of m for which the equation
(m + 4)/2 + (m + 1)x + 1 = 0 has real and
equal roots.​

Answer 1

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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

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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 :) .

Answer 2

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