For what values of k does the function f(x) = x^2 + kx - 5 have two real roots?

Given the quadratic equation f(x) = x^2 + kx
-5

We need to find the values of k where the function has 2
real roots.

We know that the function has 2 real roots when
delta > 0

delta = b^2 - 4ac >
0

==> a = 1    b= k    c =
-5

==> k^2 - 4*1*-5 >
0

==> k^2 + 20>
0

But we know that k^2 is always >
0

also 20 > 0

Then k^2
+ 20 > 0 for all real
numbers.

==> K belongs to R where R is
a real number.

==> K =
(-inf, inf)