Question

m²x²-m(5m+1)x-(5m+2)=0

Answer 1

m²x² - m.(5m + 1).x - (5m + 2) = 0

m²x² - (5m² + m).x - (5m + 2) = 0

Δ = b² - 4.a.c  

Δ = (5m² + m)² - 4 . m² . (5m + 2)  

Δ = 25m^4 + 10m³ + m² - 20m³ - 8m²

Δ = 25m^4 - 10m³ - 7m²

Há 2 raízes reais.

x = (-b +- √Δ)/2a

x' = -(5m² + m) + √(25m^4 - 10m³ - 7m²))/(2.(5m² + m))    

x'' = -(5m² + m) - √(25m^4 - 10m³ - 7m²))/(2.(5m² + m))

x' = -5m² - m + √(m²(25m² - 10m - 7)) / (10m² + m)

x'' = -5m² - m - √(m²(25m² - 10m - 7)) / (10m² + m)

x' = -5m² - m + |m|√(25m² - 10m - 7) / m.(10m + 1)    

x'' = -5m² - m - |m|√(25m² - 10m - 7) / m.(10m + 1)

x' = m.(-5m - 1 + √(25m² - 10m - 7))/m.(10m + 1)

x'' = m.(-5m - 1 - √(25m² - 10m - 7))/m.(10m + 1)

x' = (-5m - 1 + √(25m² - 10m - 7)) / (10m + 1)

x'' = (-5m - 1 - √(25m² - 10m - 7)) / (10m + 1)

x' = (5m + 2)/m

x'' = -1/m