Chapter 8: Q4. (page 520)

Which of the following is a solution to $x^{2} + 6 x - 112 = 0$ ?
F $- 14$
G $- 6$
H 6
J 12

Short Answer

Expert verified

The solution of $x^{2} + 6 x - 112 = 0$ is $x = - 14, 8$ . Hence the answer is option F.

Step by step solution

Step 1. Factor by using GCF.

Factor by using GCF to get the form $x y = 0$ .

$(x + 14) (x - 8) = 0$

Step 2. Write zero product property.

For any real numbers x and y, if $x y = 0$ then $x = 0, y = 0$ or both x and y equal to zero.

Step 3. Apply zero product property.

Apply zero product property to the equation, $(x + 14) (x - 8) = 0$ .

$x + 14 = 0 or x - 8 = 0 x = - 14 x = 8$

Therefore, the roots are $- 14$ and 8.

Step 4. Check the obtained solution.

To check whether the obtained solution is correct or not, substitute $- 14$ for x and 8 for x in the given equation and simplify.

role="math" localid="1647693760070" ${(- 14)}^{2} + 6 (- 14) - 112 \overset{?}{=} 0 0 = 0 ✓$

${(8)}^{2} + 6 (8) - 112 \overset{?}{=} 0 0 = 0 ✓$

Therefore, the obtained solution is correct. As the obtained solution completely matches with option F, option F is the required answer.

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Which of the following is a solution to $x^{2} + 6 x - 112 = 0$ ?
F $- 14$
G $- 6$
H 6
J 12

Short Answer

Step by step solution

Step 1. Factor by using GCF.

Step 2. Write zero product property.

Step 3. Apply zero product property.

Step 4. Check the obtained solution.

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Which of the following is a solution to x2+6x−112=0?F−14G-6H 6J 12

Short Answer

Step by step solution

Step 1. Factor by using GCF.

Step 2. Write zero product property.

Step 3. Apply zero product property.

Step 4. Check the obtained solution.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Mechanics Maths

Statistics

Theoretical and Mathematical Physics

Pure Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

Which of the following is a solution to $x^{2} + 6 x - 112 = 0$ ?
F $- 14$
G $- 6$
H 6
J 12