Solve p<p^2 - ScanMath

Evaluate

p < p^{2}

Move the expression to the left side

p - p^{2} < 0

Rewrite the expression

p - p^{2} = 0

Factor the expression

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p (1 - p) = 0

When the product of factors equals 0,at least one factor is 0

p = 0 1 - p = 0

Solve the equation for p

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p = 0 p = 1

Determine the test intervals using the critical values

p < 0 0 < p < 1 p > 1

Choose a value form each interval

p_{1} = - 1 p_{2} = \frac{1}{2} p_{3} = 2

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

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p < 0 is the solution p_{2} = \frac{1}{2} p_{3} = 2

To determine if 0 < p < 1 is the solution to the inequality,test if the chosen value p = \frac{1}{2} satisfies the initial inequality

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p < 0 is the solution 0 < p < 1 is not a solution p_{3} = 2

To determine if p > 1 is the solution to the inequality,test if the chosen value p = 2 satisfies the initial inequality

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p < 0 is the solution 0 < p < 1 is not a solution p > 1 is the solution

Solution

p \in (- \infty, 0) \cup (1, + \infty)

Solve the inequality