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The quadratic equation ax^2 + 8x + c = 0 has exactly one solution. If a + c = 12, and a < c, find the ordered pair (a, c).

 Oct 16, 2020
 #1
avatar+2453 
+1

Hint: Here are the possible values of a and c. Try plugging them in and solving it.

a=5, c=7

a=4, c=8

a=3, c=9

a=2, c=10

a=1, c=11

 

Tell me if you need more help :)

 
 Oct 16, 2020
 #2
avatar+27725 
+1

For one solution thie discriminant of the quadratic = 0      b^2 - 4ac = 0

                                                                                           64 - 4 ac = 0

 

so another equation relating a and c        64 - 4 ac   =     ac = 16       and given c = 12-a

                                                                                           a (12-a) = 16

                                                                                            -a^2 + 12a - 16 = 0      quadratic formula shows a = 6 -  2sqrt  5

                                                                                                                                                        and c = 6 + 2 sqrt 5

 
 Oct 16, 2020
edited by ElectricPavlov  Oct 16, 2020
 #3
avatar+2453 
+1

For future uses, the quadratic formula is:

\(\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)

 
 Oct 16, 2020
 #4
avatar+27725 
0

Thanx ! cheeky

 
ElectricPavlov  Oct 16, 2020

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