Replace F(x) with y
y=x^3-10x^2+24x
To find the roots replace y with 0.
0=x^3-10x^2-24x
Rewrite the equation as
x^3-10x^2+24x=0
Factor the left side
x(x-6)(x-4)=0
The solution is a result of
x=0, x-6=0, and x-4=0
The answer is:
x=0, 6, 4
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:
-24
Step-by-step explanation:
-1(3^2)+(-15)
-9+(-15)
-24
