Determine k so that the equation has exactly one rational solution

Question

Determine k so that the equation has exactly one rational solution x² - kx + 25 = 0.

a. ±10

b. 10

c. -10

d. None of these

Answer 1

A, B or C: 10 or -10

if k = -10

then x^2 -10x + 25 = 0

and (x-5)^2 = 0

x= 5

if k = 10

x^2 +10x +25 = 0

x=-10/2 + or - (1/2)sqr))(100-100) = -5

when the discriminate = 0, there is one unique solution

b^2 -4ac = 0

k^2 -4(1)(25) = 0

k^2 = 100

k = + or - 10