Which two values of x are roots of the polynomial below? (select all that apply
3x^2-3x+1

x = (3 + √-3) / 6 and x = (3 - √-3) / 6, so answers A and B are correct.

Step-by-step explanation:

To clarify, when we say "roots" of a quadratic expression, we're talking about it's x-intercepts, or where the entire expression = 0.  Let's start with that:

3x² - 3x + 1 = 0

Let's complete the square to solve it:

9x² - 9x + 3 = 0

9x² - 9x + 2.25 = -0.75

(3x - 1.5)² = -0.75

(3x - 3 / 2)² = -3 / 4

3x - 3 / 2 = ± i√(3 / 4)

3x - 3 / 2 = ± i√3 / 2

3x = 3 / 2 ± i√3 / 2

3x = (3 ± i√3) / 2

x = (3 ± i√3) / 6

So the x is equal to both (3 + i√3) / 6 and (3 - i√3) / 6.

You'll note that these answers don't exactly match the given ones.  The only difference there is that I factored -1 out of the radical, giving you i as a coefficient to it. You may not yet be at a point where you've covered imaginary numbers, but I assure you the answers I found here are exactly the same as x = (3 + √-3) / 6 and x = (3 - √-3) / 6.

step-by-step explanation:

i found the life tables for the year 2012. 

life table of males at age 30. probability of dying between ages x and x+1

total population:  

29–30 . . . . . . . . . . . . 0.001030

30–31 . . . . . . . . . . . . 0.001061

males:  

29–30 . . . . . . . . . . . . 0.001420

30–31 . . . . . . . . . . . . 0.001448

white population

29–30 . . . . . . . . . . . . 0.001005

30–31 . . . . . . . . . . . . 0.001037

white males

29–30 . . . . . . . . . . . . 0.001372

30–31 . . . . . . . . . . . . 0.001399

non hispanic white population

29–30 . . . . . . . . . . . . 0.001083

30–31 . . . . . . . . . . . . 0.001116

non hispanic white males

29–30 . . . . . . . . . . . . 0.001477

30–31 . . . . . . . . . . . . 0.001503

jacob, non hispanic white male. 30 years old.

probability that jacob lives to be 30 years old. 

since the given probabilities are probabilities of dying, i think we simply subtract it from 1 to get the probability of living. we will use the probability of non hispanic white male.

                                          probability of living to be 30 y.o.

29 - 30 : 1 - 0.001477 = 0.998523

30 - 31 : 1 - 0.001503 = 0.998497

kaahe btau