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.

22

step-by-step explanation:

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.