Question

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

Answer 1

c. 1; rational

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.