What is x^2e^x-3e^x<0 ?

The solution to x^2e^x-3e^x<0 is -sqrt(3)<x<sqrt(3)

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x^2e^x-3e^x<0

x^{2} e^{x} - 3 e^{x} < 0

- 3 < x < 3

Interval Notation

(- 3, 3)

Decimal Notation

- 1.73205 \dots < x < 1.73205 \dots

Solution steps

x^{2} e^{x} - 3 e^{x} < 0

Factor out common term

e^{x}

e^{x} (x^{2} - 3)

Factor

x^{2} - 3 : (x + 3) (x - 3)

= e^{x} (x + 3) (x - 3)

Find the signs of the factors of

e^{x} (x + 3) (x - 3)

Identify the intervals:

x < - 3, x = - 3, - 3 < x < 3, x = 3, x > 3

Summarize in a table:

e^{x} x + 3 x - 3 e^{x} (x + 3) (x - 3) x < - 3 + - - + x = - 3 + 0 - 0 - 3 < x < 3 + + - - x = 3 + + 00 x > 3 + + + +

Identify the intervals that satisfy the required condition:

< 0

- 3 < x < 3

∣ x + 7 ∣ < 2

\frac{2}{2 3}

1 - 64 m^{3}

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

f = 4^{- 1}