Solve -3u^2 - 1 "k" - Socratic AI (ScanMath)

Question

Factor the expression

- (3 u^{2} + 1)

Evaluate

- 3 u^{2} - 1

Solution

- (3 u^{2} + 1)

Show Solution

u_{1} = - \frac{3}{3} i, u_{2} = \frac{3}{3} i

Alternative Form

u_{1} \approx - 0.57735 i, u_{2} \approx 0.57735 i

Evaluate

- 3 u^{2} - 1

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

- 3 u^{2} - 1 = 0

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

- 3 u^{2} = 0 + 1

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

- 3 u^{2} = 1

Change the signs on both sides of the equation

3 u^{2} = - 1

Divide both sides

\frac{3 u ^{2}}{3} = \frac{- 1}{3}

Divide the numbers

u^{2} = \frac{- 1}{3}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

u^{2} = - \frac{1}{3}

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

u = \pm - \frac{1}{3}

Simplify the expression

More Steps

Evaluate

- \frac{1}{3}

Evaluate the power

\frac{1}{3} \times - 1

Evaluate the power

\frac{1}{3} \times i

Evaluate the power

More Steps

Evaluate

\frac{1}{3}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{1}{3}

Simplify the radical expression

\frac{1}{3}

Multiply by the Conjugate

\frac{3}{3 \times 3}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{3}{3}

\frac{3}{3} i

u = \pm \frac{3}{3} i

Separate the equation into 2 possible cases

u = \frac{3}{3} i u = - \frac{3}{3} i

Solution

u_{1} = - \frac{3}{3} i, u_{2} = \frac{3}{3} i

Alternative Form

u_{1} \approx - 0.57735 i, u_{2} \approx 0.57735 i

Show Solution