**High School Number Sense Lesson 93: Adding and Multiplying Roots (Combined)**

This concept builds upon our understanding of adding roots (

**AddRoots**) and multiplying roots (

**MultRoots**). It appeared

**5 times**on this year's tests, with a median placement at

**question # 43**.

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As a reminder, there are a couple of formulas that are important to remember:

- Adding roots:
**-B/A** - Multiplying roots:
**C/A**(for quadratic),**-D/A**(for cubic),**E/A**, etc.

We'll add one formula for the sum of the roots taken two at a time:

**C/A**(regardless of the degree of the polynomial).

**Example 1:**

**Let P, Q, & R be the roots of x**

^{3}- 6x^{2}+ 11x = 6. Find PQ + PR + QR. ___1. This is the sum of the roots taken two at a time, so use

**C/A**

2. C is 11, and A is 1.

3. The answer is 11/1 =

**11**

**Example 2:**

**Let P, Q, & R be the roots of x**

^{3}+ 3x^{2}- 11x = 18. Find (P + Q + R)(PQR). ___1. This will be the sum of the roots

**times**the product of the roots.

2. Sum: -B/A = -3/1 =

**-3**

3. Product: -D/A = -(-18)/1 =

**18**

4. -3 x 18 =

**-54**

**Example 3:**

**Let P, Q, & R be the roots of x**

^{3}- 7x = 6. Find (P + Q + R) + (PQR). ___1. This will be the sum of the roots

**plus**the product of the roots.

2. Sum: -B/A = -(0)/1 =

**0**

3. Product: -D/A = -(-6)/1 =

**6**

4. 0 + 6 =

**6**

**Example 4:**

**Let P, Q, & R be the roots of x**

^{3}- 3x^{2}+ 5x = 7. Find (PQR)/(P + Q + R). ___1. This will be the product of the roots

**divided by**the sum of the roots.

2. Product: -D/A = -(-7)/1 =

**7**

3. Sum: -B/A = -(-3)/1 =

**3**

4. The answer is

**7/3**

**Example 5:**

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

^{2}- x - 3 = 0 is ___1. Sum: -B/A = -(-1)/2 =

**1/2**

2. Product: C/A =

**-3/2**

3. 1/2 - (-3/2) = 4/2 =

**2**

**Up Next for High School: Ellipse**