Question

one of the roots of the quadratic equation x^2-(4+k)x+12=0

fine,
1)the roots of the equation
2)the possible values of k

please show your workings

thanks in advance.

Answer 1

x^2-(4+k)x = -12
x^2 -(4+k)x +(4+k)^2/4=-12 + (4+k)^2/4
take sqrt of each side
(x -(4+k)/2 ) =sqrt[ (4+k)^2/4-12]

ok, for the real roots, then
(4+k)^2/4-12>=0 or
(4+k)^2/4>=12 or
4+k>=sqrt24
k>=4+2 sqrt6
so k is greater than 4+2sqrt6, but sqrt 6 can be two values, or
k has to be between 4-2sqrt6 and 4+2sqrt 6

Answer 2

huh, thanks bro, but i didn't comprehen your workings.

How did you get (4+k)^2/4

Answer 3

read up on the discriminant of a quadratic: b^2-4ac