Solve k^2-4<0 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve the inequality by separating into cases

Solve for k

- 2 < k < 2

Alternative Form

k \in (- 2, 2)

Evaluate

k^{2} - 4 < 0

Rewrite the expression

k^{2} - 4 = 0

Move the constant to the right-hand side and change its sign

k^{2} = 0 + 4

Removing 0 doesn't change the value,so remove it from the expression

k^{2} = 4

Take the root of both sides of the equation and remember to use both positive and negative roots

k = \pm 4

Simplify the expression

More Steps

k = \pm 2

Separate the equation into 2 possible cases

k = 2 k = - 2

Determine the test intervals using the critical values

k < - 2 - 2 < k < 2 k > 2

Choose a value form each interval

k_{1} = - 3 k_{2} = 0 k_{3} = 3

To determine if k < - 2 is the solution to the inequality,test if the chosen value k = - 3 satisfies the initial inequality

More Steps

k < - 2 is not a solution k_{2} = 0 k_{3} = 3

To determine if - 2 < k < 2 is the solution to the inequality,test if the chosen value k = 0 satisfies the initial inequality

More Steps

k < - 2 is not a solution - 2 < k < 2 is the solution k_{3} = 3

To determine if k > 2 is the solution to the inequality,test if the chosen value k = 3 satisfies the initial inequality

More Steps

k < - 2 is not a solution - 2 < k < 2 is the solution k > 2 is not a solution

Solution

- 2 < k < 2

Alternative Form

k \in (- 2, 2)

Show Solution