Answer:
x = -2, x = 3 − i√8, and x = 3 + i√8
Step-by-step explanation:
g(x) = x³ − 4x² − x + 22
This is a cubic equation, so it must have either 1 or 3 real roots.
Using rational root theorem, we can check if any of those real roots are rational. Possible rational roots are ±1, ±2, ±11, and ±22.
g(-1) = 18
g(1) = 18
g(-2) = 0
g(2) = 12
g(-11) = 1782
g(11) = 858
g(-22) = -12540
g(22) = 8712
We know -2 is a root. The other two roots are irrational. To find them, we must find the other factor of g(x). We can do this using long division, or we can factor using grouping.
g(x) = x³ − 4x² − 12x + 11x + 22
g(x) = x (x² − 4x − 12) + 11 (x + 2)
g(x) = x (x − 6) (x + 2) + 11 (x + 2)
g(x) = (x (x − 6) + 11) (x + 2)
g(x) = (x² − 6x + 11) (x + 2)
x² − 6x + 11 = 0
Quadratic formula:
x = [ 6 ± √(36 − 4(1)(11)) ] / 2
x = (6 ± 2i√8) / 2
x = 3 ± i√8
The three roots are x = -2, x = 3 − i√8, and x = 3 + i√8.
Answer:
x=4 and y=3
Step-by-step explanation:
put one of the equations in slope form and solve
But it's not one doesn't always have to be the gcf
Answer:
c the ratio of the measure of arc QR and the circle
Step-by-step explanation:
i just took the quiz
hope this helps (:
Answer:
The LCM of 9, 12, and 24, is <em>72. </em>
Step-by-step explanation:
To find the answer you must figure out the factors of <em>each number</em>, and see which factor has the <em>same number.</em>
<u><em>Factors of 9: </em></u> <u><em>Factors of 12:</em></u><em> </em><u><em>Factors of 24: </em></u>
<em> 9 12 24</em>
<em> 18 24 48</em>
<em> 27 36 72</em>
<em> 36 48</em>
<em> 45 60</em>
<em> 54 72</em>
<em> 63</em>
<em> 72</em>
When we look at all these factors, none of them have the same number <em>except 72.</em> Since <em>all</em> of these factors have <em>72 in them</em>, this is the<em> </em>LCM of 9, 12, and 24.
