Standard form
ok, so the factored form of a polynomial with roots r1,r2,r3,r4 is
f(x)=(x-r1)(x-r2)(x-r3)(x-r4)
so
since the roots are 0,1,-2i,3+√3
I am assuming you want real coefients so ince -2i is a root, 2i is also a root
f(x)=(x-0)(x-1)(x+2i)(x-2i)(x-(3+√3))
f(x)=x⁵-(√3)x⁴-4x⁴+(√3)x³+7x³-(4√3)x²-16x²+12x
if you were allowed to have no-real coefients then exclue the 2i
f(x)=(x-0)(x-1)(x+2i)(x-(3+√3))
f(x)=
So, you start by separating the equation into two inequalities and you get
4x+1 > -7 and 4x +1 < 5
Solve these inequalities and you get your final answer:
x > -2 and x < 1
(The equalities symbols are supposed to have the "or equal" line beneath them, I was just too lazy to put them.)
Answer:
53.008
Step-by-step explanation:
6255/118
The answer would be positive so ignore the negatives.
Set up a proportion:
1/7 L of water - 1/9 of the aquarium
x L of water - 1 aquarium (the whole aquarium)
![\frac{\frac{1}{7}}{\frac{1}{9}}=\frac{x}{1} \\ \\ \frac{1}{7} \times 9=x \\ \\ \frac{9}{7}=x \\ \\ x=1 \frac{2}{7}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cfrac%7B1%7D%7B7%7D%7D%7B%5Cfrac%7B1%7D%7B9%7D%7D%3D%5Cfrac%7Bx%7D%7B1%7D%20%5C%5C%20%5C%5C%0A%5Cfrac%7B1%7D%7B7%7D%20%5Ctimes%209%3Dx%20%5C%5C%20%5C%5C%0A%5Cfrac%7B9%7D%7B7%7D%3Dx%20%5C%5C%20%5C%5C%0Ax%3D1%20%5Cfrac%7B2%7D%7B7%7D)
1 2/7 liters of water are needed to fill the aquarium.