Solve t^4-5t^2 4 - ScanMath

Question

Simplify the expression

t^{4} - 20 t^{2}

Evaluate

t^{4} - 5 t^{2} \times 4

Solution

t^{4} - 20 t^{2}

Show Solution

t^{2} (t^{2} - 20)

Evaluate

t^{4} - 5 t^{2} \times 4

Multiply the terms

t^{4} - 20 t^{2}

Rewrite the expression

t^{2} \times t^{2} - t^{2} \times 20

Solution

t^{2} (t^{2} - 20)

Show Solution

t_{1} = - 25, t_{2} = 0, t_{3} = 25

Alternative Form

t_{1} \approx - 4.472136, t_{2} = 0, t_{3} \approx 4.472136

Evaluate

t^{4} - 5 t^{2} \times 4

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

t^{4} - 5 t^{2} \times 4 = 0

Multiply the terms

t^{4} - 20 t^{2} = 0

Factor the expression

t^{2} (t^{2} - 20) = 0

Separate the equation into 2 possible cases

t^{2} = 0 t^{2} - 20 = 0

The only way a power can be 0 is when the base equals 0

t = 0 t^{2} - 20 = 0

Solve the equation

More Steps

Evaluate

t^{2} - 20 = 0

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

t^{2} = 0 + 20

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

t^{2} = 20

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

t = \pm 20

Simplify the expression

More Steps

Evaluate

20

Write the expression as a product where the root of one of the factors can be evaluated

4 \times 5

Write the number in exponential form with the base of 2

2^{2} \times 5

The root of a product is equal to the product of the roots of each factor

2^{2} \times 5

Reduce the index of the radical and exponent with 2

25

t = \pm 25

Separate the equation into 2 possible cases

t = 25 t = - 25

t = 0 t = 25 t = - 25

Solution

t_{1} = - 25, t_{2} = 0, t_{3} = 25

Alternative Form

t_{1} \approx - 4.472136, t_{2} = 0, t_{3} \approx 4.472136

Show Solution