+0

0
91
4

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
+2197
0

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
+28025
+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
+2197
0

For future uses, the quadratic formula is:

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

Oct 16, 2020
#4
+28025
0

Thanx !

ElectricPavlov  Oct 16, 2020