Solving Quadratic Equations Using Common Factors Practice

Question

Complete this assessment to review what you’ve learned. It will not count toward your grade.

One of the steps needed to solve a quadratic equation by grouping is to split the middle rem 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.

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 want to find two numbers \( a \) and \( b \) such that:

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

From the factors of 42, we can list the pairs of integers:

• (1, 42)
• (2, 21)
• (3, 14)
• (6, 7)
• (-1, -42)
• (-2, -21)
• (-3, -14)
• (-6, -7)

Among these pairs, the combination that adds up to -13 is:

• \( -6 \) and \( -7 \) (because \(-6 + -7 = -13\))

Thus, the two numbers needed to complete the step are \(-7\) and \(-6\).

Since you asked for the lesser value first, the answer is:

-6, -7