Kami Export - Seth Boucher - Jan 20 A - 11.3 Complex Solutions of Quadratic Equations____11.pdf

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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 = b​2​ - 4ac x​2​ - 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. 2x​2​ - 5x + 4 = 0 D = 25 - 32 = -7 < 0 2 non real solutions Solve the equations using quadratic formula. 4. x​2​ - 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 2x​2​ + 3x + 5 = 0 x = -3 ±i√ 31 x = -3 ± √ 9 − 4 ( 2 ) ( 5 ) 4 2(2) x = -3 ± √ 9 − 40 4 6. 4x​2​ - 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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