Solve 2t^4-7t^2-4

Question

Factor the expression

(t - 2) (t + 2) (2 t^{2} + 1)

Evaluate

2 t^{4} - 7 t^{2} - 4

Rewrite the expression

2 t^{4} + (1 - 8) t^{2} - 4

Calculate

2 t^{4} + t^{2} - 8 t^{2} - 4

Rewrite the expression

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

Factor out t^{2} from the expression

t^{2} (2 t^{2} + 1) - 4 \times 2 t^{2} - 4

Factor out - 4 from the expression

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

Factor out 2 t^{2} + 1 from the expression

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

Solution

(t - 2) (t + 2) (2 t^{2} + 1)

Show Solution

t_{1} = - \frac{2}{2} i, t_{2} = \frac{2}{2} i, t_{3} = - 2, t_{4} = 2

Alternative Form

t_{1} \approx - 0.707107 i, t_{2} \approx 0.707107 i, t_{3} = - 2, t_{4} = 2

Evaluate

2 t^{4} - 7 t^{2} - 4

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

2 t^{4} - 7 t^{2} - 4 = 0

Factor the expression

(t - 2) (t + 2) (2 t^{2} + 1) = 0

Separate the equation into 3 possible cases

t - 2 = 0 t + 2 = 0 2 t^{2} + 1 = 0

Solve the equation

More Steps

Evaluate

t - 2 = 0

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

t = 0 + 2

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

t = 2

t = 2 t + 2 = 0 2 t^{2} + 1 = 0

Solve the equation

More Steps

Evaluate

t + 2 = 0

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

t = 0 - 2

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

t = - 2

t = 2 t = - 2 2 t^{2} + 1 = 0

Solve the equation

More Steps

Evaluate

2 t^{2} + 1 = 0

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

2 t^{2} = 0 - 1

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

2 t^{2} = - 1

Divide both sides

\frac{2 t ^{2}}{2} = \frac{- 1}{2}

Divide the numbers

t^{2} = \frac{- 1}{2}

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

t^{2} = - \frac{1}{2}

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

t = \pm - \frac{1}{2}

Simplify the expression

More Steps

Evaluate

- \frac{1}{2}

Evaluate the power

\frac{1}{2} \times - 1

Evaluate the power

\frac{1}{2} \times i

Evaluate the power

\frac{2}{2} i

t = \pm \frac{2}{2} i

Separate the equation into 2 possible cases

t = \frac{2}{2} i t = - \frac{2}{2} i

t = 2 t = - 2 t = \frac{2}{2} i t = - \frac{2}{2} i

Solution

t_{1} = - \frac{2}{2} i, t_{2} = \frac{2}{2} i, t_{3} = - 2, t_{4} = 2

Alternative Form

t_{1} \approx - 0.707107 i, t_{2} \approx 0.707107 i, t_{3} = - 2, t_{4} = 2

Show Solution