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
To split the middle term, we need to find two numbers that are both factors of the coefficient of the x-term (-13) and whose sum is equal to that same coefficient.
In this case, the factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42. Checking through these factors, we find that 6 and 7 have a sum of 13, which matches the coefficient of the x-term.
Therefore, the two numbers needed to complete this step are 6 and 7.
Not the answer it was wrkng
Apologies for the confusion. Let's solve it again correctly.
Given the equation x^2 - 13x + 42 = 0, we need to split the middle term (-13x) as a sum of two terms.
To find the two numbers, we need to identify two factors of the constant term (42) whose sum is equal to the coefficient of the x-term (-13).
The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, and 42.
Checking these factors, we find that -6 and -7 have a sum of -13, which matches the coefficient of the x-term.
Therefore, the two numbers needed to complete this step are -6 and -7.
Still wrong
Apologies for the confusion. Let's solve it again correctly.
Given the equation x^2 - 13x + 42 = 0, we need to split the middle term (-13x) as a sum of two terms.
To find the two numbers, we need to identify two factors of the coefficient of the x-term (-13) whose product is equal to the product of the constant term (42) and the coefficient of the x^2 term (1).
The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, and 42.
Now, let's check these factors:
1 * 42 = 42 (not equal to -13), not a valid pair
2 * 21 = 42 (not equal to -13), not a valid pair
3 * 14 = 42 (not equal to -13), not a valid pair
6 * 7 = 42 (equal to -13), a valid pair!
Therefore, the two numbers needed to complete this step are 6 and 7.
Apologies for the incorrect response earlier.
To solve a quadratic equation by grouping, we need to split the middle term, which is -13x in this case, as a sum of two terms. The quadratic equation is x^2 - 13x + 42 = 0.
To find the two numbers, we need to factorize the quadratic equation. Since the coefficient of x^2 is 1, we are looking for two numbers whose product is equal to the constant term, which is 42, and whose sum is equal to the coefficient of x, which is -13.
One way to find these two numbers is to list all possible pairs of factors of 42 and check if their sum is -13. The factors of 42 are 1, 2, 3, 6, 7, 14, 21, and 42.
Checking their sums:
1 + 42 = 43 (not -13)
2 + 21 = 23 (not -13)
3 + 14 = 17 (not -13)
6 + 7 = 13 (not -13)
Since the sum of -13 cannot be obtained by adding any two of these factors, it means that the quadratic equation x^2 - 13x + 42 = 0 cannot be factored, at least not with whole numbers.
Therefore, the two numbers needed to split the middle term as a sum of two terms in this case is not possible with whole numbers.