Review for TEST #2: Topics are: 1)Rationalize the denominators. 2)Solving quadratic equations, using the quadratic formula. 3)Power of i. 4)Operations.

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Review for TEST #2: Topics are: 1)Rationalize the denominators. 2)Solving quadratic equations, using the quadratic formula. 3)Power of i. 4)Operations on Complex Numbers. 5)Discriniminant 6)Sum and Product of the roots of quadratic equations.

Aim: How do we prepare for TEST #2? Do Now: ? Solve: 1) x² – 3x = 9 2) 3x² – 4x + 2 = 0 3) Simplify: : are

Part I: Rationalize the denominators Simplify:

Part II: Solving Quadratic Equations, using the Quadratic formula ? Solve: 1) x² + 8x + 25 = 0 2)4x² – 12x + 25 = 0 3) x² + 7 = 2x

Clock 4 System 1 - i i Remainder of 0 Remainder of 1 Remainder of 2 Remainder of 3 Part III: Power of i

? Simplify the following: 1)i 8 + i 9 + i 10 + i 11 2)i 16 + i 6 – 2 i 5 + i 13

Part IV: Operations on complex numbers ? 1 ) Subtract (12 + 3i) from (3 – i), and then graph the result. Simplify: 4) Find the product of (6 – 2i) and i.

Part V:Discriminant Value of DiscriminantType and Number of Roots Example of Graph of Related Function b 2 – 4ac > 0 b 2 – 4ac is a perfect square. 2 real, rational roots b 2 – 4ac > 0 b 2 – 4ac is not a perfect square. 2 real, irrational roots b 2 – 4ac = 0 1 real, rational root b 2 – 4ac < 02 complex roots

Part V:Discriminant 1) The roots of the equation x² – 7x+ 15 = 0 a) Imaginary b) real, rational, and equal c) real, rational, and unequal d) real, irrational, and unequal are 2) The roots of the equation 2x² – x = 4 a) Imaginary b) real, rational, and equal c) real, rational, and unequal d) real, irrational

Part VI: Sum and Product of the roots 1)Find the sum and product of roots; 3x² – 2x – 15 = 0 2)Write a quadratic equation whose roots are; a) 6i and – 6i b)

Find the second root, r 2 #1: If one root of x 2 – 6x + k = 0 is 4 #2: If one root of x 2 – kx + 18 = 0 is 6

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