GP1PAPS2HW4Solutions Skill 2b Day 2: Solving Quadratic Equations Use the discriminant to state the number and types of solutions to the following equations. 1. 2! + 6− 7 = 2 discriminant = ! − 4= 108, which is positive and not a perfect square There are two distinct real irrational solutions. 2. 3! + 4+ 1 = 0 discriminant = ! − 4= 4, which is positive and a perfect square There are two distinct real rational solutions. 3. 5! + 20= 0 discriminant = ! − 4= 400, which is positive and a perfect square There are two distinct real rational solutions. 4. 3! + 12+ 14 = 2 discriminant = ! − 4= 0 There is exactly one real rational solution. 5. 5! + 2 = 4discriminant = ! − 4= −24, which is negative There are two distinct complex solutions (a complex conjugate pair). 6. ! + 6 = 0 discriminant = ! − 4= −24, which is negative There are two distinct complex solutions (a complex conjugate pair). Determine the value of c that will complete the square. 7. ! − 14+ = −14 2 ! = 49 8. ! + 27+ = !" ! ! = !"# !
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GP1-‐PAP-‐S2-‐HW4-‐Solutions Skill 2b Day 2: Solving Quadratic Equations
Use the discriminant to state the number and types of solutions to the following equations. 1. 2𝑎! + 6𝑎 − 7 = 2 discriminant = 𝑏! − 4𝑎𝑐 = 108, which is positive and not a perfect square There are two distinct real irrational solutions. 2. 3𝑥! + 4𝑥 + 1 = 0 discriminant = 𝑏! − 4𝑎𝑐 = 4, which is positive and a perfect square There are two distinct real rational solutions. 3. 5𝑥! + 20𝑥 = 0 discriminant = 𝑏! − 4𝑎𝑐 = 400, which is positive and a perfect square There are two distinct real rational solutions. 4. 3𝑎! + 12𝑎 + 14 = 2 discriminant = 𝑏! − 4𝑎𝑐 = 0 There is exactly one real rational solution. 5. 5𝑦! + 2 = 4𝑦 discriminant = 𝑏! − 4𝑎𝑐 = −24, which is negative There are two distinct complex solutions (a complex conjugate pair). 6. 𝑐! + 6 = 0 discriminant = 𝑏! − 4𝑎𝑐 = −24, which is negative There are two distinct complex solutions (a complex conjugate pair). Determine the value of c that will complete the square. 7. 𝑥! − 14𝑥 + 𝑐