Up to multiples, if you're given the roots you can write the polynomial by multiplying several parenthesis in the form
![(x-x_0)](https://tex.z-dn.net/?f=%28x-x_0%29)
where
is a root. So, in your case, you have
![f(x) = a(x+6)(x+5)(x+1)](https://tex.z-dn.net/?f=f%28x%29%20%3D%20a%28x%2B6%29%28x%2B5%29%28x%2B1%29)
We can fix the parameter a by imposing f(0)=60:
![f(0)=a(0+6)(0+5)(0+1)=30a=60\iff a=2](https://tex.z-dn.net/?f=f%280%29%3Da%280%2B6%29%280%2B5%29%280%2B1%29%3D30a%3D60%5Ciff%20a%3D2)
So, your polynomial is
![f(x) = 2(x+6)(x+5)(x+1)=2x^3+24x^2+82x+60](https://tex.z-dn.net/?f=f%28x%29%20%3D%202%28x%2B6%29%28x%2B5%29%28x%2B1%29%3D2x%5E3%2B24x%5E2%2B82x%2B60)
Answer:
Step-by-step explanation:
Hello, if I take the following
2, 2, -5, 2, 2, -5, 2, 2, -5, 2, 2
The sum is 8*2-5*3=16-15=1 > 0
and
2 + 2 -5 < 0
2 - 5 + 2 < 0
-5 + 2 + 2 < 0
2 + 2 -5 < 0
2 - 5 + 2 < 0
-5 + 2 + 2 < 0
2 + 2 -5 < 0
2 - 5 + 2 < 0
-5 + 2 + 2 < 0
2 + 2 -5 < 0
2 - 5 + 2 < 0
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
9 m³
Step-by-step explanation:
The formula for calculating the volume (V) of a cuboid is
V = depth × width × height
= 1.8 × 2.5 × 2 = 9 m³
Answer:
13) b
14) d
15) b
16 a
Step-by-step explanation: hope this helps :)
<span>my answer to you would be that for this kind of a sequence, there is a fixed way of finding the nth term value
let's get these basics straight first:
1) Un= the nth term value
for eg. U1 = 1st term value
2) a = first term
3) d = difference
Ok now the first step to finding the nth term is finding the constant difference
in the example that you gave the constant difference is 1.5
ie 1.5 is being added on each time
now the fixed rule for finding the nth term is :
Un = a + d(n-1)
why?
because let's take a common example of a linear sequence, a sequence with a constant first term ( so called because it forms a line when drawn in a graph):
first term is a so,
a, a+d, a+2d, a+3d......a(n-1)d
(because the coefficient of d is one less than the term number)
so putting this into your q:
a = 5.5
d=1.5
Un=a + d (n-1)
Un=5.5 + 1.5(n-1)
Un=5.5 + 1.5n - 1.5
Un=4+ 1.5n
there you go it works...
for other types like quadratic cubic and geometric progression, its a totally different story
</span>