**Unformatted text preview: **1/20 IM2
Name: 11.3 Complex Solutions of Quadratic Equations
Period: State the number of solutions and whether they are real or non-real
No.
1. Equation Discriminant
D = b2 - 4ac x2 - 11x + 18 = 0 Answer D = 121 - 72 = 49 > 0 2 2 real solutions 2. x + 8x + 16 = 0 D = 64 - 64 = 0 = 0 1 real solution 3. 2x2 - 5x + 4 = 0 D = 25 - 32 = -7 < 0 2 non real solutions Solve the equations using quadratic formula.
4. x2 - 2x + 4 = 0 x = 2 ± √ 22 − 4 ( 1 ) ( 4 ) x = 2 ± √ −12 2(1) 2 x = 2 ± √ 4 − 16 x = 2 ± 2i √ 3 2
5. 2 x = 2(1 ± i √ 3 )
2
x = 1+ i√ 3
x = 1−i√ 3 2x2 + 3x + 5 = 0 x = -3 ±i√ 31 x = -3 ± √ 9 − 4 ( 2 ) ( 5 ) 4 2(2)
x = -3 ± √ 9 − 40
4
6. 4x2 - 2x + 3 = 0 x = 2 ± √ 4 − 48
8
x = 2 ± √ −44
2 x = 2 ±2i√ 11 x = 1 ±i√ 11 2 x = 2(1 ±i√ 11 )
2 x = 1 +i√ 11
x = 1 −i√ 11 ...

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