Question

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 x2−13x+42=0
, which two numbers would be needed to complete this step? Enter the lesser value first.(1 point)
x2−13x+42=0

x2+
x+
x+42=0

Answer 1

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 (42) and add up to the coefficient of the middle term (-13).

We are looking for two numbers \( a \) and \( b \) such that:

1. \( a \times b = 42 \)
2. \( a + b = -13 \)

After evaluating the factor pairs of 42:

• \( 1 \times 42 \)
• \( 2 \times 21 \)
• \( 3 \times 14 \)
• \( 6 \times 7 \)

None of these pairs sum to -13 when both are negative.

However, if we take the pairs \( -6 \) and \( -7 \):

• \( (-6) + (-7) = -13 \)
• \( (-6) \times (-7) = 42 \)

Thus, the two numbers we need to split the middle term are \(-6\) and \(-7\).

So, the answer is:

−7 and −6.