What is the answer to m^2e^{mx}+6me^{mx}+5e^{mx}=0 ?

The answer to m^2e^{mx}+6me^{mx}+5e^{mx}=0 is No Solution for x\in\mathbb{R}

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m^2e^{mx}+6me^{mx}+5e^{mx}=0

m^{2} e^{m x} + 6 m e^{m x} + 5 e^{m x} = 0

No Solution for x \in R

Solution steps

m^{2} e^{m x} + 6 m e^{m x} + 5 e^{m x} = 0

Factor

m^{2} e^{m x} + 6 m e^{m x} + 5 e^{m x} : e^{m x} (m^{2} + 6 m + 5)

e^{m x} (m^{2} + 6 m + 5) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

e^{m x} = 0

a^{f (x)}

cannot be zero or negative for

x \in R

No Solution for x \in R

- 2 e^{2 x} = 0

e^{2 x} + 1 = 3 e^{- x}

5^{5 x - 2} = 45

6^{x} = 3^{x + 2}

What is the answer to m^2e^{mx}+6me^{mx}+5e^{mx}=0 ?
The answer to m^2e^{mx}+6me^{mx}+5e^{mx}=0 is No Solution for x\in\mathbb{R}