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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 = 4 discriminant = ! 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 + = !" ! ! = !"# !

# GP1\$PAP\$S2\$HW4\$Solutions2 Skill22b2Day22

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GP1-PAP-S2-HW4-SolutionsGP1-­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.      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 = 4     discriminant = ! − 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
= −5 2
= 25 4
Solve  the  following  quadratic  equations  by  completing  the  square.    Give  exact  answers.   10.    ! − 14 + 40 = 0       ! − 14 = −40      ! − 14 + 49 = −40 + 49     − 7 ! = 9     − 7 = ±3     = 4, = 10           11.    ! − 6 =  15     ! − 6 + 9 =  15 + 9         − 3 ! = 24       − 3 = ± 24     − 3 = ± 4 6     = 3 ± 2 6       12.    2! + 8 = 10     ! + 4 = 5     ! + 4 + 4 = 5 + 4     + 2 ! = 9     + 2 = ±3     = −5, = 1
GP1-­PAP-­S2-­HW4-­Solutions   13.    4! − 5 = −1     4!
4 − 5 4 = −1 4

14.    3! + 6 + 10 = 0         3! + 6 = −10     3!
3 + 6 3 = −10 3

+ 1 3 3

GP1-­PAP-­S2-­HW4-­Solutions         15.    4! − 12 + 9 = 0       4! − 12 = −9     4!
4 − 12 4

8 + 10 8

GP1-­PAP-­S2-­HW4-­Solutions                                                                                   17.  −8! − 2 = −3 − 10! + 27     2! + = 27     2!
2 + 2 = 27 2

= 27 2 8 8 + 1 16

2 − 3 2 = −51 2

GP1-­PAP-­S2-­HW4-­Solutions                                                                                                       19.  8! + 6 = −7 − 77     8! + 13 = −77     8!
8 + 13 8 ##### GP1 USER GUIDE - VIDAUimages.adeal.com.au/m_pdf/USER MANUALS/GP1+ - WP... · GP1+ 产品保修卡 稳拍 02 Introduction WENPOD GP1+ is the state of the art digital gyroscopic stabilizer
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