Solving Word Problems Involving Quadratic Equations

Do Now: Write a “let” statement and equation for each example. Explain the difference.

A. Find two consecutive integers whose sum is 13.

Let x = first integer

x + 1 = second integer

x + x + 1 = 13

B. Find two consecutive integers whose product is 42.

Let x = first integer

x + 1 = second integer

x(x + 1) = 42

How do we solve consecutive integer problems?

Write “let” statement (if consecutive integers, use x;x+1;x+2. If consecutive even or odd, use x;x+2:x+4)

Write equation using key words from statement: sum (add), product (multiply), more than (add), less than (subtract), etc.

Solve equation

Check in original problem statement

Practice p. 774-775 10,12

10. Let x = first odd integer

x + 2 = second odd integer

x(x + 2) = 143

x2 + 2x = 143

x2 + 2x – 143 = 0

(x + 13)(x – 11) = 0

x = - 13 x = 11

Integers: -13 and – 11

11 and 13

12. Let x = first integer

x + 1 = second integer

x + 2 = third integer

(x + 1)(x + 2) = 30

x2 + 3x + 2 = 30

x2 + 3x – 28 = 0

(x + 7)(x – 4) = 0

x = - 7 x = 4

Integers: -7, - 6, - 5

4, 5, 6

How do we solve word problems?Practice p. 774 #2

Let x = the number

x2 – 9x = 36

x2 – 9x – 36 = 0

(x – 12)(x + 3) = 0

x – 12 = 0 x + 3 = 0

x = 12 x = - 3

How do we solve area problems?(what is the formula for area of a rectangle?

1. Draw diagram

2. Label information

3. Write formula

4. Substitute and solve

The length of a rectangular garden is 6 more than the width. The area is 27 sq. units. Find the dimensions of the

garden.

x(x + 6) = 27x2 + 6x = 27x2 + 6x – 27 = 0(x + 9)(x – 3) = 0x + 9 = 0 x – 3 = 0x = - 9 x = 3REJECTDimensions: 3, 9