Solve x^4+3x^2-4 - Socratic AI (ScanMath)

Question

Factor the expression

(x - 1) (x + 1) (x^{2} + 4)

Evaluate

x^{4} + 3 x^{2} - 4

Rewrite the expression

x^{4} + (4 - 1) x^{2} - 4

Calculate

x^{4} + 4 x^{2} - x^{2} - 4

Rewrite the expression

x^{2} \times x^{2} + x^{2} \times 4 - x^{2} - 4

Factor out x^{2} from the expression

x^{2} (x^{2} + 4) - x^{2} - 4

Factor out - 1 from the expression

x^{2} (x^{2} + 4) - (x^{2} + 4)

Factor out x^{2} + 4 from the expression

(x^{2} - 1) (x^{2} + 4)

Solution

(x - 1) (x + 1) (x^{2} + 4)

Show Solution

x_{1} = - 2 i, x_{2} = 2 i, x_{3} = - 1, x_{4} = 1

Evaluate

x^{4} + 3 x^{2} - 4

To find the roots of the expression,set the expression equal to 0

x^{4} + 3 x^{2} - 4 = 0

Factor the expression

(x - 1) (x + 1) (x^{2} + 4) = 0

Separate the equation into 3 possible cases

x - 1 = 0 x + 1 = 0 x^{2} + 4 = 0

Solve the equation

More Steps

Evaluate

x - 1 = 0

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

x = 0 + 1

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

x = 1

x = 1 x + 1 = 0 x^{2} + 4 = 0

Solve the equation

More Steps

Evaluate

x + 1 = 0

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

x = 0 - 1

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

x = - 1

x = 1 x = - 1 x^{2} + 4 = 0

Solve the equation

More Steps

Evaluate

x^{2} + 4 = 0

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

x^{2} = 0 - 4

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

x^{2} = - 4

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

x = \pm - 4

Simplify the expression

More Steps

Evaluate

- 4

Evaluate the power

4 \times - 1

Evaluate the power

4 \times i

Evaluate the square root

2 i

x = \pm 2 i

Separate the equation into 2 possible cases

x = 2 i x = - 2 i

x = 1 x = - 1 x = 2 i x = - 2 i

Solution

x_{1} = - 2 i, x_{2} = 2 i, x_{3} = - 1, x_{4} = 1

Show Solution