SOLUTION: Find all values of k that ensure that the given equation has exactly one solution. (Enter your answers as a comma-separated list.)
kx2 + 34x + k = 0
Algebra ->
Equations
-> SOLUTION: Find all values of k that ensure that the given equation has exactly one solution. (Enter your answers as a comma-separated list.)
kx2 + 34x + k = 0
Log On
Question 1189683: Find all values of k that ensure that the given equation has exactly one solution. (Enter your answers as a comma-separated list.)
kx2 + 34x + k = 0 Answer by ikleyn(52775) (Show Source):
You can put this solution on YOUR website! .
Find all values of k that ensure that the given equation has exactly one solution. (Enter your answers as a comma-separated list.)
kx2 + 34x + k = 0
~~~~~~~~~~~~~~~~~~~~~
The necessary and sufficient condition is that the discriminant of the quadratic equation is zero
d = b^2 - 4ac = 0,
or
34^2 - 4k^2 = 0,
which gives
k^2 =
k = +/- = +/- = +/- 17.
ANSWER. There are two values of k satisfying the imposed condition: k = 17 and k = -17.
