Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Ask your questions and receive detailed answers from professionals with extensive experience in various fields. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
To solve the quadratic equation [tex]\( x^2 + 10x + 21 = 0 \)[/tex], we can use the factorization method.
Step-by-Step Solution:
1. Write down the quadratic equation:
[tex]\[ x^2 + 10x + 21 = 0 \][/tex]
2. Factorize the quadratic expression:
To factor the quadratic expression, we look for two numbers that multiply to the constant term (21) and add up to the linear coefficient (10).
3. Find the factors of 21 that add up to 10:
- The factors of 21 are (1, 21), (3, 7), and their respective negative pairs.
- We need the pair that adds up to 10:
[tex]\[ 3 + 7 = 10 \][/tex]
Therefore, the numbers are 3 and 7.
4. Write the quadratic expression as a product of binomials:
[tex]\[ x^2 + 10x + 21 = (x + 3)(x + 7) \][/tex]
5. Set each factor equal to zero and solve for [tex]\( x \)[/tex]:
[tex]\[ (x + 3)(x + 7) = 0 \][/tex]
This gives us two equations:
[tex]\[ x + 3 = 0 \quad \text{or} \quad x + 7 = 0 \][/tex]
6. Solve each equation for [tex]\( x \)[/tex]:
[tex]\[ x + 3 = 0 \implies x = -3 \][/tex]
[tex]\[ x + 7 = 0 \implies x = -7 \][/tex]
So, the solutions to the quadratic equation [tex]\( x^2 + 10x + 21 = 0 \)[/tex] are [tex]\( x = -3 \)[/tex] and [tex]\( x = -7 \)[/tex].
Answer:
A. [tex]\( x = -3 \)[/tex]; [tex]\( x = -7 \)[/tex]
Step-by-Step Solution:
1. Write down the quadratic equation:
[tex]\[ x^2 + 10x + 21 = 0 \][/tex]
2. Factorize the quadratic expression:
To factor the quadratic expression, we look for two numbers that multiply to the constant term (21) and add up to the linear coefficient (10).
3. Find the factors of 21 that add up to 10:
- The factors of 21 are (1, 21), (3, 7), and their respective negative pairs.
- We need the pair that adds up to 10:
[tex]\[ 3 + 7 = 10 \][/tex]
Therefore, the numbers are 3 and 7.
4. Write the quadratic expression as a product of binomials:
[tex]\[ x^2 + 10x + 21 = (x + 3)(x + 7) \][/tex]
5. Set each factor equal to zero and solve for [tex]\( x \)[/tex]:
[tex]\[ (x + 3)(x + 7) = 0 \][/tex]
This gives us two equations:
[tex]\[ x + 3 = 0 \quad \text{or} \quad x + 7 = 0 \][/tex]
6. Solve each equation for [tex]\( x \)[/tex]:
[tex]\[ x + 3 = 0 \implies x = -3 \][/tex]
[tex]\[ x + 7 = 0 \implies x = -7 \][/tex]
So, the solutions to the quadratic equation [tex]\( x^2 + 10x + 21 = 0 \)[/tex] are [tex]\( x = -3 \)[/tex] and [tex]\( x = -7 \)[/tex].
Answer:
A. [tex]\( x = -3 \)[/tex]; [tex]\( x = -7 \)[/tex]
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.