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Answer :
To solve the problem of finding two consecutive odd integers whose product is 2,115, we can follow these steps:
1. Understanding Consecutive Odd Integers:
- Consecutive odd integers follow a pattern where if one integer is [tex]\( x \)[/tex], the next consecutive odd integer can be expressed as [tex]\( x + 2 \)[/tex].
2. Setting Up the Equation:
- We know the product of these two integers is 2,115. Therefore, we can write the equation:
[tex]\[
x \cdot (x + 2) = 2,115.
\][/tex]
3. Expanding the Equation:
- Expand the expression on the left side:
[tex]\[
x^2 + 2x = 2,115.
\][/tex]
4. Formulating the Quadratic Equation:
- To solve for [tex]\( x \)[/tex], we need to set the equation to zero:
[tex]\[
x^2 + 2x - 2,115 = 0.
\][/tex]
5. Choosing the Correct Quadratic Equation:
- The possible quadratic equations from the options are:
- [tex]\( x^2 + 2x - 2,115 = 0 \)[/tex]
- [tex]\( x^2 + x - 2,115 = 0 \)[/tex]
- [tex]\( x^2 + 2x + 2,115 = 0 \)[/tex]
- The equation we derived is [tex]\( x^2 + 2x - 2,115 = 0 \)[/tex]. So, this is the correct quadratic equation that could be used to solve the word problem.
Thus, the correct quadratic equation is [tex]\( x^2+2x-2,115=0 \)[/tex]. Solving this equation would give the values of [tex]\( x \)[/tex], which represent the two consecutive odd integers.
1. Understanding Consecutive Odd Integers:
- Consecutive odd integers follow a pattern where if one integer is [tex]\( x \)[/tex], the next consecutive odd integer can be expressed as [tex]\( x + 2 \)[/tex].
2. Setting Up the Equation:
- We know the product of these two integers is 2,115. Therefore, we can write the equation:
[tex]\[
x \cdot (x + 2) = 2,115.
\][/tex]
3. Expanding the Equation:
- Expand the expression on the left side:
[tex]\[
x^2 + 2x = 2,115.
\][/tex]
4. Formulating the Quadratic Equation:
- To solve for [tex]\( x \)[/tex], we need to set the equation to zero:
[tex]\[
x^2 + 2x - 2,115 = 0.
\][/tex]
5. Choosing the Correct Quadratic Equation:
- The possible quadratic equations from the options are:
- [tex]\( x^2 + 2x - 2,115 = 0 \)[/tex]
- [tex]\( x^2 + x - 2,115 = 0 \)[/tex]
- [tex]\( x^2 + 2x + 2,115 = 0 \)[/tex]
- The equation we derived is [tex]\( x^2 + 2x - 2,115 = 0 \)[/tex]. So, this is the correct quadratic equation that could be used to solve the word problem.
Thus, the correct quadratic equation is [tex]\( x^2+2x-2,115=0 \)[/tex]. Solving this equation would give the values of [tex]\( x \)[/tex], which represent the two consecutive odd integers.
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