To determine the cost of each item, we need to set up equations. From the problem statement, we have three unknowns so we need three equations. We set up equations as follows:
let x cost of small pizzas
y cost of soda
z cost of salad
two small pizzas, a liter of soda, and a salad cost $14
2x + y + z = 14
one small pizza, a liter of soda, and three salads cost $15
x + y + 3z = 15
three small pizzas, a liter of soda, and two salads cost $22
3x + y + 2z = 22
Solving for x, y and z, we will have:
x = $ 5
y = $ 1
z = $ 3
Two distinct roots means two real solutions for x (the parabola needs to cross the x-axis twice)
Vertex form of a quadratic equation: (h,k) is vertex
y = a(x-h)^2 + k
The x of the vertex needs to equal 3
y = a(x-3)^2 + k
In order to have two distinct roots the parabola must be (+a) upward facing with vertex below the x-axis or (-a) downward facing with vertex above the x-axis. Parabolas are symmetrical so for an easy factorable equation make "a" 1 or -1 depending on if you want the upward/downward facing one.
y = (x-3)^2 - 1
Vertex (3,-1) upwards facing with two distinct roots 4 and 2
y = x^2 -6x + 9 - 1
y = x^2 -6x + 8
y = (x - 4)(x - 2)
As of 12:04 EST U.S.
$1=<span>112.624847Yen
So:
100USD(112.624847Y/1USD)=11262.62 Yen</span>
You have the following expression given in the problem:
f(x) = x³ – 2x²<span> – x + 2
Therefore, to find the roots, you must apply the proccedure shown below:
1. You have:
0 </span><span>= x3 – 2x2 – x + 2
2. Then, when you factor, you obtain:
(x-2)(x-1)(x+1)=0
3. Therefore, you have that the roots are the following:
x1=-1
x2=1
x3=2</span>