Solving Quadratic Equations Using the Quadratic Formula

Part 2

Solving Quadratic Equations Using the Quadratic Formula

Example:

Eliminate the fractions by multiplying by 8.x2 – 8x + 20 = 0 a = 1, b = -8, and c = 20

.

. .

there is no solution

since is negatives s

2( 8) ( 8) 4(1)(20)2(1)

x

8 64 802

x

2 42

b b acxa

8 16

2x

21 5 08 2

Solve x x

Solving Quadratic Equations Using the Quadratic Formula

40102 101010

5

x

x

x

10 10. . ,5 5

s s

0 0 4010

x

Example: 5w2 = 2 a = 5, b = -2, and c = 0

5w2 – 2 = 0

20 0 4(5)( 2)2(5)

x

2 42

b b acxa

Solving Quadratic Equations Using the Quadratic Formula

Example: Find three positive consecutive evenintegers whose squares have a sum of 2360.

Let the three positive consecutive even integers be x, x + 2, and x + 4.

Then x2 + (x + 2)2 + (x + 4)2 = 2360x2 + x2 + 4x + 4 + x2 + 8x + 16 = 23603x2 + 12x – 2340 = 0 x2 + 4x – 780 = 0

Solving Quadratic Equations Using the Quadratic Formula

x2 + 4x – 780 = 0 a = 1, b = 4, and c = 780

4 562

x

4 31362

x

2 42

b b acxa

2(4) (4) 4(1)(780)2(1)

x

4 16 31202

x

x = 26 or x = -30

Since our integers must be positive, it must be x = 26. Therefore, the integers are 26, 28, and 30.

Homework

Do # 9, 10, 12, 15, 16, 17, 19, 22 on page174 from Section 5.8 for Friday May 15th

Don’t forget to hand in Assignment #2