Using the discriminant, how many solutions and what type of solution (s) does k^2-10k+25=0 have?

a. 2; irrational

b. 2; rational

c. 1; rational

d. no real solutions

c. 1; rational

Step-by-step explanation:

k² - 10k + 25 = 0

The discriminant of ax² + bx + c is b² - 4ac.

If the discriminant is negative, there are no real roots.

If the discriminant is zero, there is 1 real root.

If the discriminant is positive, there are 2 real roots.

If the discriminant is a perfect square, the root (s) are rational.

If the discriminant isn't a perfect square, the root (s) are irrational.

Finding the discriminant:

a = 1, b = - 10, c = 25

(-10) ² - 4 (1) (25) = 0

The discriminant is zero, so there is 1 rational root.