Using the discriminant, how many solutions and what type of solution (s) does 3p-9p^2=6 have?

a. 2; irrational

b. 2; rational

c. 1; rational

d. no real solutions

d. no real solutions

Step-by-step explanation:

3p - 9p² = 6

0 = 9p² - 3p + 6

0 = 3p² - p + 2

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 = 3, b = - 1, c = 2

(-1) ² - 4 (3) (2) = - 23

The discriminant is negative, so there are no real roots.