The roots of the equation 5x^2 - kx + 1 = 0 are real and distinct. Calculate all posible values of k.

The roots of the equation 5x^2 - kx + 1 = 0 are real and
distinct, when the discriminant of the equation, delta, will be
positive.

delta = b^2 - 4*a*c, where a,b,c are the
coefficients of the equation.

Let's identify
a,b,c:

a = 5

b =
-k

c = 1

delta = (k)^2 -
4*1*5

delta > 0 => k^2 - 20 >
0

k^2 - 20 = 0

We'll add 20
both sides:

k^2 =20

k1 = +sqrt
20

k2 = -sqrt 20

k1 =
+2sqrt5

k2 = -2sqrt5

Delta is
positive and the equation has 2 distinct real roots when k is in the
intervals:

(-inf., -2sqrt5) U
(2sqrt5,+inf.)