Question

find m if the quadratic equation x^2-2(m+1)x+m^2 has equal and real roots

Answer 1

Answer:

m = -1/2

Step-by-step explanation:

Discriminant

Let a quadratic equation be ax² + bx + c = 0

Discriminant Δ = b² - 4 ac

Conditions

For equal roots

b² = 4 ac

For real roots

b² > 4 ac

For imaginary roots

b² < 4 ac

Given they have equal roots .

Comparing x² - 2 ( m + 1 ) x + m² with ax² + bx + c

a = 1

b =  - 2 ( m + 1 )

c = m²

b² = 4 ac

⇒ ( - 2 )²( m + 1 )² = 4 . 1 . m²

⇒ 4 ( m + 1 )² = 4 m²

⇒ ( m + 1 )² = m²

⇒ m² + 2 m + 1 = m²

⇒ 2 m + 1 = 0

⇒ 2 m = - 1

⇒ m = -1/2

Answer 2

Answer:

m = -1/2


Step-by-step explanation:


Discriminant


Let a quadratic equation be ax² + bx + c = 0

Discriminant Δ = b² - 4 ac


Conditions


For equal roots

b² = 4 ac


For real roots

b² > 4 ac


For imaginary roots

b² < 4 ac


Given they have equal roots .


Comparing x² - 2 ( m + 1 ) x + m² with ax² + bx + c


a = 1

b =  - 2 ( m + 1 )

c = m²


b² = 4 ac

⇒ ( - 2 )²( m + 1 )² = 4 . 1 . m²

⇒ 4 ( m + 1 )² = 4 m²

⇒ ( m + 1 )² = m²

⇒ m² + 2 m + 1 = m²

⇒ 2 m + 1 = 0

⇒ 2 m = - 1

⇒ m = -1/2


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