What is the discriminant and number of solutions to the problem- y=2x2+6x+12

Δ = b² - 4ac
Δ = (6)² - 4(2)(12)
Δ = 36 - 4(24)
Δ = 36 - 96
Δ = -60

y = 2x² + 6x + 12
0 = 2x² + 6x + 12
0 = 2(x²) + 2(3x) + 2(6)
0 = 2(x² + 3x + 6)
2              2
0 = x² + 3x + 6
x = -(3) ± √((3)² - 4(1)(6))
                   2(1)
x = -3 ± √(9 - 4(6))
                2
x = -3 ± √(9 - 24)
              2
x = -3 ± √(-15)
             2
x = -3 ± i√(15)
             2
x = -1.5 ± 0.5i√(15)
x = -1.5 + 0.5i√(15)    or    x = -1.5 - 0.5i√(15)

The discriminant is -60 and the number of solutions is 2.

The 95% confidence interval for the mean is between 14.88 hours to 15.12 hours.

Step-by-step explanation:

We have been given:

Sample size or n = 1000

Sample mean = 15 hours

Population standard deviation or s = 2 hours

We will use z distribution to find the confidence interval about the mean.

z value for 95% confidence interval is 1.96.

So, the interval is :

and

Solving this we get, 14.88 and 15.12

So, the 95% confidence interval for the mean is between 14.88 hours to 15.12 hours.