Solve x^2 2x<0 - ScanMath

Evaluate

x^{2} \times 2 x < 0

Multiply

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2 x^{3} < 0

Rewrite the expression

2 x^{3} = 0

Rewrite the expression

x^{2} \times 2 x = 0

Multiply both sides

x^{2} \times 2 x \times \frac{1}{2} = 0 \times \frac{1}{2}

Calculate

x^{2} \times x = 0

Separate the equation into 2 possible cases

x^{2} = 0 x = 0

The only way a power can be 0 is when the base equals 0

x = 0 x = 0

Find the union

x = 0

Determine the test intervals using the critical values

x < 0 x > 0

Choose a value form each interval

x_{1} = - 1 x_{2} = 1

To determine if x < 0 is the solution to the inequality,test if the chosen value x = - 1 satisfies the initial inequality

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x < 0 is the solution x_{2} = 1

To determine if x > 0 is the solution to the inequality,test if the chosen value x = 1 satisfies the initial inequality

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x < 0 is the solution x > 0 is not a solution

Solution

x < 0

Alternative Form

x \in (- \infty, 0)

Solve the inequality