**High School Number Sense Lesson 42: Adding the Roots of a Polynomial**

Last week we covered

**MultRoots**. Today we will introduce its companion concept. This one appeared

**10 times**this year, with a median placement at

**question # 45**.

**Number Dojo Level: 288**

Unlike with multiplying roots, the formula for adding roots stays the same (

**-B/A**), regardless of the degree of the polynomial. As a reminder:

**A**is the coefficient connected to the highest power of the variable, and**B**is the coefficient connected to the second-highest power of the variable.

**-B/A**.

**Example 1:**

**The sum of the roots of 3x**

^{2}+ 6x + 4 = 0 is ___1. Written as Ax

^{2}+ Bx + C, A =

**3**and B =

**6**.

2. The sum of the roots is

**-B/A**, which is

**-6/3**=

**-2**.

**Example 2:**

**The sum of the roots of 2x**

^{2}- 10x + 7 = 0 is ___1. Written as Ax

^{2}+ Bx + C, A =

**2**and B =

**-10**.

2. The sum of the roots is

**-B/A**, which is

**-(-10)/2**=

**5**.

**Example 3:**

**If P and Q are the roots of 4x**

^{2}- 2x + 5 = 0, then P + Q = ___1. Written as Ax

^{2}+ Bx + C, A =

**4**and B =

**-2**.

2. The sum of the roots is

**-B/A**, which is

**-(-2)/4**=

**1/2**.

**Example 4:**

**The sum of the roots of (2x + 3)**

^{2}= 0 is ___1. Multiply (2x + 3) by (2x + 3) to get

**4x**.

^{2}+ 12x + 92. Written as Ax

^{2}+ Bx + C, A =

**4**and B =

**12**.

3. The sum of the roots is

**-B/A**, which is

**-12/4**=

**-3**.

**Example 5:**

**The sum of the roots of 3x**

^{3}- 2x + 4 = 0 is ___1. Be careful! Written as Ax

^{3}+ Bx

^{2}+ Cx + D, A =

**3**and B =

**0**.

*There is no x*.

^{2}term2. The sum of the roots is

**-B/A**, which is

**-0/3**=

**0**.

**Here's a free worksheet to help you practice AddRoots:**

addroots.pdf |

**Up Next for High School: FactorialOper**