Solved on Mar 24, 2024

Solve for $u$ where $u(u-6)=0$ . Write the solutions as integers or simplified fractions.

STEP 1

1. The equation $u(u-6)=0$ is a quadratic equation in standard form.
2. The Zero Product Property states that if a product of two factors is zero, then at least one of the factors must be zero.
3. The solutions for $u$ can be integers or fractions in simplest form.

STEP 2

1. Apply the Zero Product Property to solve for $u$ .
2. Simplify the solutions to their simplest form.

STEP 3

Apply the Zero Product Property, which states that if a product equals zero, then at least one of the factors must be zero.
$u(u-6) = 0 \Rightarrow u = 0 \text{ or } (u-6) = 0$

STEP 4

Solve the first equation $u = 0$ .
$u = 0$

STEP 5

Solve the second equation $(u-6) = 0$ for $u$ .
$u - 6 = 0 \Rightarrow u = 6$

STEP 6

Write the solutions for $u$ in simplest form.
The solutions from STEP_2 and STEP_3 are already in simplest form, as they are integers.
$u = 0 \text{ or } u = 6$
The solutions for $u$ are:
$u = 0$
$\text{ or } u = 6$

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Solve for $u$ where $u(u-6)=0$ . Write the solutions as integers or simplified fractions.

STEP 1

1. The equation $u(u-6)=0$ is a quadratic equation in standard form.
2. The Zero Product Property states that if a product of two factors is zero, then at least one of the factors must be zero.
3. The solutions for $u$ can be integers or fractions in simplest form.

STEP 2

1. Apply the Zero Product Property to solve for $u$ .
2. Simplify the solutions to their simplest form.

STEP 3

Apply the Zero Product Property, which states that if a product equals zero, then at least one of the factors must be zero.
$u(u-6) = 0 \Rightarrow u = 0 \text{ or } (u-6) = 0$

STEP 4

Solve the first equation $u = 0$ .
$u = 0$

STEP 5

Solve the second equation $(u-6) = 0$ for $u$ .
$u - 6 = 0 \Rightarrow u = 6$

STEP 6

Write the solutions for $u$ in simplest form.
The solutions from STEP_2 and STEP_3 are already in simplest form, as they are integers.
$u = 0 \text{ or } u = 6$
The solutions for $u$ are:
$u = 0$
$\text{ or } u = 6$

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Solve for uuu where u(u−6)=0u(u-6)=0u(u−6)=0. Write the solutions as integers or simplified fractions.

STEP 1

1. The equation u(u−6)=0u(u-6)=0u(u−6)=0 is a quadratic equation in standard form.2. The Zero Product Property states that if a product of two factors is zero, then at least one of the factors must be zero.3. The solutions for uuu can be integers or fractions in simplest form.

STEP 2

1. Apply the Zero Product Property to solve for uuu.2. Simplify the solutions to their simplest form.

STEP 3

Apply the Zero Product Property, which states that if a product equals zero, then at least one of the factors must be zero.u(u−6)=0⇒u=0 or (u−6)=0 u(u-6) = 0 \Rightarrow u = 0 \text{ or } (u-6) = 0 u(u−6)=0⇒u=0 or (u−6)=0

STEP 4

Solve the first equation u=0u = 0u=0.u=0 u = 0 u=0

STEP 5

Solve the second equation (u−6)=0(u-6) = 0(u−6)=0 for uuu.u−6=0⇒u=6 u - 6 = 0 \Rightarrow u = 6 u−6=0⇒u=6

STEP 6

Write the solutions for uuu in simplest form.The solutions from STEP_2 and STEP_3 are already in simplest form, as they are integers.u=0 or u=6 u = 0 \text{ or } u = 6 u=0 or u=6The solutions for uuu are:u=0 u = 0 u=0 or u=6 \text{ or } u = 6 or u=6

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Solve for $u$ where $u(u-6)=0$ . Write the solutions as integers or simplified fractions.

1. The equation $u(u-6)=0$ is a quadratic equation in standard form.
2. The Zero Product Property states that if a product of two factors is zero, then at least one of the factors must be zero.
3. The solutions for $u$ can be integers or fractions in simplest form.

1. Apply the Zero Product Property to solve for $u$ .
2. Simplify the solutions to their simplest form.

Apply the Zero Product Property, which states that if a product equals zero, then at least one of the factors must be zero.
$u(u-6) = 0 \Rightarrow u = 0 \text{ or } (u-6) = 0$

Solve the first equation $u = 0$ .
$u = 0$

Solve the second equation $(u-6) = 0$ for $u$ .
$u - 6 = 0 \Rightarrow u = 6$

Write the solutions for $u$ in simplest form.
The solutions from STEP_2 and STEP_3 are already in simplest form, as they are integers.
$u = 0 \text{ or } u = 6$
The solutions for $u$ are:
$u = 0$
$\text{ or } u = 6$