Question

explain why 3x^2 + kx - 1 is never always positive for any value of k

Answer 1

the formula of discriminant is b^2 - 4ac

in this case:
a=3
b=k
c= -1

so, k^2 always has positive value,

then k^2 (positive number) -4 * 3 * (-1)= k -(-12)= k^2 + 12.

positive number + positive number = always positive number

Answer 2

so 3x^2 + kx - 1 is always positive for any value of k