If a polynomial P(x) has a zero equal to
a, then (x-a) is a factor of this polynomial. So if a polynomial has zeros
a,
b and
c then it has we could write:
P(x)=(x-a)(x-b)(x-c).
Here we can clearly see that a, making the left hand side 0 because of the factor (x-a), makes the left hand side 0 as well. This means that P(a)=0. This illustrates the discussion above.
Thus, substituting a, b, c with <span>−3, 3, 2 we can write P(x)=(x+3)(x-3)(x-2).
We can expand the right hand side to have the polynomial in standard form:
</span>
![=(x^2-9)(x-2)=x^3-2x^2-9x+18](https://tex.z-dn.net/?f=%3D%28x%5E2-9%29%28x-2%29%3Dx%5E3-2x%5E2-9x%2B18)
We see that all conditions are satisfied.
<span>
Answer: </span>
![P(x)=x^3-2x^2-9x+18](https://tex.z-dn.net/?f=P%28x%29%3Dx%5E3-2x%5E2-9x%2B18)
<span>
</span>
Answer:
It will take 8 hours for Frank and Mary to get to the beach
Step-by-step explanation:
Step 1: Give expression for calculating
d=s×t
where;
d=distance traveled i miles
s=speed in miles per hour
t=time in hours
in our case;
d=520 miles
s=65 miles per hour
t=unknown
Step 2: Solve for the unknown, t
In order to solve for t, the expressions can be rearranged as follows ;
t=d/s
replacing values for d and s;
t=520/65
t=8 hours
It will take 8 hours for Frank and Mary to get to the beach
Answer:
Length = ![5\ \text{ft}](https://tex.z-dn.net/?f=5%5C%20%5Ctext%7Bft%7D)
Breadth = ![5\ \text{ft}](https://tex.z-dn.net/?f=5%5C%20%5Ctext%7Bft%7D)
Step-by-step explanation:
Let
be the length of the garden
and
be the width of the garden
From the details of the cost in the question we get
![20x+2\times (10y)=200\\\Rightarrow 20x+20y=200\\\Rightarrow x+y=\dfrac{200}{20}\\\Rightarrow x+y=10\\\Rightarrow y=10-x](https://tex.z-dn.net/?f=20x%2B2%5Ctimes%20%2810y%29%3D200%5C%5C%5CRightarrow%2020x%2B20y%3D200%5C%5C%5CRightarrow%20x%2By%3D%5Cdfrac%7B200%7D%7B20%7D%5C%5C%5CRightarrow%20x%2By%3D10%5C%5C%5CRightarrow%20y%3D10-x)
Now area of the garden is
![A=xy\\\Rightarrow A=x(10-x)\\\Rightarrow A=10x-x^2](https://tex.z-dn.net/?f=A%3Dxy%5C%5C%5CRightarrow%20A%3Dx%2810-x%29%5C%5C%5CRightarrow%20A%3D10x-x%5E2)
Differentiating with respect to x we get
![\dfrac{dA}{dx}=10-2x](https://tex.z-dn.net/?f=%5Cdfrac%7BdA%7D%7Bdx%7D%3D10-2x)
Equating with 0
![0=10-2x\\\Rightarrow x=\dfrac{-10}{-2}\\\Rightarrow x=5](https://tex.z-dn.net/?f=0%3D10-2x%5C%5C%5CRightarrow%20x%3D%5Cdfrac%7B-10%7D%7B-2%7D%5C%5C%5CRightarrow%20x%3D5)
Double derivative of the area is
![\dfrac{d^2A}{dx^2}=-2](https://tex.z-dn.net/?f=%5Cdfrac%7Bd%5E2A%7D%7Bdx%5E2%7D%3D-2%3C0)
So, area is maximum at ![x=5](https://tex.z-dn.net/?f=x%3D5)
![y=10-x=10-5\\\Rightarrow y=5](https://tex.z-dn.net/?f=y%3D10-x%3D10-5%5C%5C%5CRightarrow%20y%3D5)
So, the length and breadth of the rectangle is
.
Answer:
choice b d and e
Step-by-step explanation:
2/7 srry if I'm wrong because they are parellel and possibly the same