What are the solutions to the equation x^2+2(m-1)x+(m+5)=0 ?

The solutions to the equation x^2+2(m-1)x+(m+5)=0 are x=-m+1+sqrt(m^2-3m-4),x=-m+1-sqrt(m^2-3m-4)

Find the zeros of x^2+2(m-1)x+(m+5)=0

The zeros of x^2+2(m-1)x+(m+5)=0 are x=-m+1+sqrt(m^2-3m-4),x=-m+1-sqrt(m^2-3m-4)

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x^{2} + 2 (m - 1) x + (m + 5) = 0

x = - m + 1 + m^{2} - 3 m - 4, x = - m + 1 - m^{2} - 3 m - 4

Solution steps

x^{2} + 2 (m - 1) x + (m + 5) = 0

Expand

x^{2} + 2 (m - 1) x + (m + 5) : x^{2} + 2 m x - 2 x + m + 5

x^{2} + 2 m x - 2 x + m + 5 = 0

Write in the standard form

a x^{2} + b x + c = 0

x^{2} + (2 m - 2) x + m + 5 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( 2 m - 2 ) \pm ( 2 m - 2 ) ^{2} - 4 \cdot 1 \cdot ( m + 5 )}{2 \cdot 1}

Simplify

(2 m - 2)^{2} - 4 \cdot 1 \cdot (m + 5) : 2 m^{2} - 3 m - 4

x_{1, 2} = \frac{- ( 2 m - 2 ) \pm 2 m ^{2} - 3 m - 4}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( 2 m - 2 ) + 2 m ^{2} - 3 m - 4}{2 \cdot 1}, x_{2} = \frac{- ( 2 m - 2 ) - 2 m ^{2} - 3 m - 4}{2 \cdot 1}

x = \frac{- ( 2 m - 2 ) + 2 m ^{2} - 3 m - 4}{2 \cdot 1} : - m + 1 + m^{2} - 3 m - 4

x = \frac{- ( 2 m - 2 ) - 2 m ^{2} - 3 m - 4}{2 \cdot 1} : - m + 1 - m^{2} - 3 m - 4

The solutions to the quadratic equation are:

x = - m + 1 + m^{2} - 3 m - 4, x = - m + 1 - m^{2} - 3 m - 4

x, f (2 x - 1) = 4 x^{2} - 10 x + a

m^{2} + \frac{m}{2} - \frac{3}{2} = 0

y, 8 x^{3} + 3 y^{2} + 6 x + 5 y = 0

x^{2} - 20 x + a^{2} = 0

2 x^{2} + 4 - 3 x = 0

What are the solutions to the equation x^2+2(m-1)x+(m+5)=0 ?
The solutions to the equation x^2+2(m-1)x+(m+5)=0 are x=-m+1+sqrt(m^2-3m-4),x=-m+1-sqrt(m^2-3m-4)
Find the zeros of x^2+2(m-1)x+(m+5)=0
The zeros of x^2+2(m-1)x+(m+5)=0 are x=-m+1+sqrt(m^2-3m-4),x=-m+1-sqrt(m^2-3m-4)