Math / Algebra

QuestionSolve the equation. $(x-4)(x-6)=0$
The solution set is $\square$ (Type integers or fractions. Use a comma to separate answers as needed.)

Studdy Solution

STEP 1

1. The equation is a factored quadratic equation.
2. The zero product property can be applied, which states that if a product of factors equals zero, at least one of the factors must be zero.

STEP 2

1. Apply the zero product property.
2. Solve each equation for $x$ .
3. Write the solution set.

STEP 3

Apply the zero product property. Since the product of two factors is zero, set each factor equal to zero:
$(x-4) = 0 \quad \text{or} \quad (x-6) = 0$

STEP 4

Solve each equation for $x$ :
For $(x-4) = 0$ : $x = 4$
For $(x-6) = 0$ : $x = 6$

STEP 5

Write the solution set. The solutions are $x = 4$ and $x = 6$ . Therefore, the solution set is:
$\{4, 6\}$
The solution set is: $\boxed{4, 6}$

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QuestionSolve the equation. $(x-4)(x-6)=0$
The solution set is $\square$ (Type integers or fractions. Use a comma to separate answers as needed.)

Studdy Solution

STEP 1

1. The equation is a factored quadratic equation.
2. The zero product property can be applied, which states that if a product of factors equals zero, at least one of the factors must be zero.

STEP 2

1. Apply the zero product property.
2. Solve each equation for $x$ .
3. Write the solution set.

STEP 3

Apply the zero product property. Since the product of two factors is zero, set each factor equal to zero:
$(x-4) = 0 \quad \text{or} \quad (x-6) = 0$

STEP 4

Solve each equation for $x$ :
For $(x-4) = 0$ : $x = 4$
For $(x-6) = 0$ : $x = 6$

STEP 5

Write the solution set. The solutions are $x = 4$ and $x = 6$ . Therefore, the solution set is:
$\{4, 6\}$
The solution set is: $\boxed{4, 6}$

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QuestionSolve the equation. (x−4)(x−6)=0(x-4)(x-6)=0(x−4)(x−6)=0The solution set is □\square□ (Type integers or fractions. Use a comma to separate answers as needed.)

Studdy Solution

STEP 1

1. The equation is a factored quadratic equation.2. The zero product property can be applied, which states that if a product of factors equals zero, at least one of the factors must be zero.

STEP 2

1. Apply the zero product property.2. Solve each equation for x x x.3. Write the solution set.

STEP 3

Apply the zero product property. Since the product of two factors is zero, set each factor equal to zero:(x−4)=0or(x−6)=0 (x-4) = 0 \quad \text{or} \quad (x-6) = 0 (x−4)=0or(x−6)=0

STEP 4

Solve each equation for x x x:For (x−4)=0 (x-4) = 0 (x−4)=0: x=4 x = 4 x=4For (x−6)=0 (x-6) = 0 (x−6)=0: x=6 x = 6 x=6

STEP 5

Write the solution set. The solutions are x=4 x = 4 x=4 and x=6 x = 6 x=6. Therefore, the solution set is:{4,6} \{4, 6\} {4,6} The solution set is: 4,6\boxed{4, 6}4,6​

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QuestionSolve the equation. $(x-4)(x-6)=0$
The solution set is $\square$ (Type integers or fractions. Use a comma to separate answers as needed.)

1. The equation is a factored quadratic equation.
2. The zero product property can be applied, which states that if a product of factors equals zero, at least one of the factors must be zero.

1. Apply the zero product property.
2. Solve each equation for $x$ .
3. Write the solution set.

Apply the zero product property. Since the product of two factors is zero, set each factor equal to zero:
$(x-4) = 0 \quad \text{or} \quad (x-6) = 0$

Solve each equation for $x$ :
For $(x-4) = 0$ : $x = 4$
For $(x-6) = 0$ : $x = 6$

Write the solution set. The solutions are $x = 4$ and $x = 6$ . Therefore, the solution set is:
$\{4, 6\}$
The solution set is: $\boxed{4, 6}$