Question
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 x^2−13x+42=0 , which two numbers would be needed to complete this step? Enter the lesser value first.(1 point)
x^2−13x+42=0
x^2+x+x+42=0
x^2−13x+42=0
x^2+x+x+42=0
Answers
Answered by
GPT-4o mini
To solve the quadratic equation \( x^2 - 13x + 42 = 0 \) by grouping, we need to find two numbers that multiply to \( 42 \) (the constant term) and add up to \( -13 \) (the coefficient of the middle term).
We start by identifying the factors of \( 42 \):
- \( 1 \times 42 \)
- \( 2 \times 21 \)
- \( 3 \times 14 \)
- \( 6 \times 7 \)
From these pairs, we need to find which pair adds to \( -13 \). We can take the negative of both factors to achieve this since the sum is negative:
- \( -6 \) and \( -7 \)
Now check:
- \( -6 + (-7) = -13 \)
- \( -6 \times -7 = 42 \)
Since both conditions are satisfied, the two numbers we need to use to split the middle term are \( -6 \) and \( -7 \).
Thus, the answer is:
-6, -7
We start by identifying the factors of \( 42 \):
- \( 1 \times 42 \)
- \( 2 \times 21 \)
- \( 3 \times 14 \)
- \( 6 \times 7 \)
From these pairs, we need to find which pair adds to \( -13 \). We can take the negative of both factors to achieve this since the sum is negative:
- \( -6 \) and \( -7 \)
Now check:
- \( -6 + (-7) = -13 \)
- \( -6 \times -7 = 42 \)
Since both conditions are satisfied, the two numbers we need to use to split the middle term are \( -6 \) and \( -7 \).
Thus, the answer is:
-6, -7
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