Duplicate Question
The question on this page has been marked as a duplicate question.
Original Question
One of the steps needed to solve a quadratic equation by grouping just to split the middle term as the sum of two terms given t...Asked by Smartypants
One of the steps needed to solve a quadratic equation by grouping is to split the middle term as a sum of two terms. Given the equation x2−13x+42=0, which two numbers would be needed to complete this step? Enter the lesser value first.(1 point)x2−13x+42=0x2+x+x+42=0
Answers
Answered by
GPT-4o mini
To solve the quadratic equation \( x^2 - 13x + 42 = 0 \) by factoring through grouping, we need to find two numbers that multiply to the constant term (which is 42) and add up to the coefficient of the linear term (which is -13).
1. Identify the product: \( 42 \)
2. Identify the sum: \( -13 \)
We need to find two numbers that satisfy these conditions.
The pairs of factors of \( 42 \) are:
- \( 1 \) and \( 42 \)
- \( 2 \) and \( 21 \)
- \( 3 \) and \( 14 \)
- \( 6 \) and \( 7 \)
Out of these pairs, we need to identify which pair sums to \( -13 \).
Considering the negatives:
- \( -6 \) and \( -7 \) multiply to \( 42 \) and add to \( -13 \).
Thus, the two numbers we are looking for are \( -6 \) and \( -7 \).
So the answer, entering the lesser value first, is:
\[
-7, -6
\]
1. Identify the product: \( 42 \)
2. Identify the sum: \( -13 \)
We need to find two numbers that satisfy these conditions.
The pairs of factors of \( 42 \) are:
- \( 1 \) and \( 42 \)
- \( 2 \) and \( 21 \)
- \( 3 \) and \( 14 \)
- \( 6 \) and \( 7 \)
Out of these pairs, we need to identify which pair sums to \( -13 \).
Considering the negatives:
- \( -6 \) and \( -7 \) multiply to \( 42 \) and add to \( -13 \).
Thus, the two numbers we are looking for are \( -6 \) and \( -7 \).
So the answer, entering the lesser value first, is:
\[
-7, -6
\]
There are no human answers yet. A form for humans to post answers is coming very soon!