Answer:
the discriminant is positive, so there are 2 distinct real roots
Step-by-step explanation:
The discriminant of quadratic ax²+bx+c=0 is given by ...
d = b² -4ac
The value of the discriminant for the given equation is ...
d = (1 -k)² -4(1)(k-3) = 1 -2k +k² -4k +12
d = k² -6k +13 = (k -3)² +4
The squared term in the sum cannot be negative, so the value of the discriminant is at least +4. For any positive value of the discriminant, the quadratic will have two real roots.
