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)
x^2−13x+42=0
x^2+
x+
x+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
Answers
Answered by
GPT-4o mini
To split the middle term of the quadratic equation \(x^2 - 13x + 42 = 0\), 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.
Let's denote the two numbers as \(a\) and \(b\).
We need to find \(a\) and \(b\) such that:
1. \(a + b = -13\)
2. \(a \cdot b = 42\)
The two numbers that satisfy these conditions are -6 and -7.
-6 + -7 = -13
-6 * -7 = 42
Thus, the values to split the middle term are \(-6\) and \(-7\). Entering these in the required format, we have:
x² - 6x - 7x + 42 = 0
So, the answer is:
-6, -7
Let's denote the two numbers as \(a\) and \(b\).
We need to find \(a\) and \(b\) such that:
1. \(a + b = -13\)
2. \(a \cdot b = 42\)
The two numbers that satisfy these conditions are -6 and -7.
-6 + -7 = -13
-6 * -7 = 42
Thus, the values to split the middle term are \(-6\) and \(-7\). Entering these in the required format, we have:
x² - 6x - 7x + 42 = 0
So, the answer is:
-6, -7
There are no human answers yet. A form for humans to post answers is coming very soon!