10.1back.notebook
10.1 back: Solving quadratic equations
Recall: No perfect square number can be under the radical
4, 9, 16, 25, 36, 49 ...
√75
√15
√ ­9
You can't take the square root of a negative number
(­)(­) = +
(+)(+)=+
1
10.1back.notebook
Since we can't take the square root of a negative number, we made up an imaginary number we call i so that: i = √­1
√­49
√49 √­1
7i
If you have a number and i you put the number first
Just like 3x, 3i
The standard form of an complex numbers is: a + bi
8 ­ 2i
2 + 3i√7
7 ­ √5
2
10.1back.notebook
Remember, you always have two solutions to a radical, one positive and one negative. You can use the ± symbol. So instead of writing x = 3 or x = ­3 you could write x = ± 3
√16
√­49
3
10.1back.notebook
x2 + 32 = 0
2(x ­ 5)2 + 30 = 0
4
10.1back.notebook
10.1 back # Mo3
3) ±3i
10.1 front # Mo3
3) x2 + 3x + 2 = 0
6) ±3
6) x2 ­ 4 = 0
9) ± 5i√2
9) x2 ­7x + 6 = 0
12) ­3, 1
12) x2 ­ x = 0
15) 2/3, 0
15) 4x2 ­ 7x ­ 2 = 0
18) ­4 ± 2i√7
18) 4x2 ­ x ­ 3 = 0
21) 3 ± 5√2
21) 3x2 ­ 4x + 1 = 0
24) ­1/2 ± 3√5
24) 8x2 ­ 10x ­ 3 = 0
27) 6x2 ­ 7x ­ 5 = 0
5