Solve a > a^2 - ScanMath

Evaluate

a > a^{2}

Move the expression to the left side

a - a^{2} > 0

Rewrite the expression

a - a^{2} = 0

Factor the expression

More Steps

a (1 - a) = 0

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

a = 0 1 - a = 0

Solve the equation for a

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a = 0 a = 1

Determine the test intervals using the critical values

a < 0 0 < a < 1 a > 1

Choose a value form each interval

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

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

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a < 0 is not a solution a_{2} = \frac{1}{2} a_{3} = 2

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

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

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

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

Solution

0 < a < 1

Alternative Form

a \in (0, 1)

Solve the inequality