Answer:
15
Step-by-step explanation:
Answer:
The top right option.
Step-by-step explanation:
Answer:
(x^4) - 64x
Step-by-step explanation:
zeros at 4 and 0 are the roots so can be factor as x*(x-4) and the multiplicity tels to what power you have to raise those factors
becuase multiplicity of 1 for root at 0, and multiplicity of 3 at root 4
now to write this in standard form
Answer:
Step-by-step explanation:
First we define two generic vectors in our space:
By definition we know that Euclidean norm on an 2-dimensional Euclidean space is:
Also we know that the inner product in space is defined as:
So as first condition we have that both two vectors have Euclidian Norm 1, that is:
and
As second condition we have that:
Which is the same:
Replacing the second condition on the first condition we have:
Since we have two posible solutions, or . If we choose , we can choose next the other solution for .
Remembering,
The two vectors we are looking for are:
Answer: x = {-4, -1, 2}
<u>Step-by-step explanation:</u>
q p
F(x) = x³ + 3x² - 6x - 8
Possible rational roots are: +/- {1, 2, 4, 8}
F(1) = (1)³ + 3(1)² - 6(1) - 8
= 1 + 3 - 6 - 8
= -10 <em>Since the remainder is not 0, then x = 1 is not a root</em>
F(-1) = (-1)³ + 3(-1)² - 6(-1) - 8
= -1 + 3 + 6 - 8
= 0 <em>Since the remainder is 0, x = -1 is a root.</em>
Use synthetic division to find the remaining factor:
x = -1 → x + 1 = 0
-1 | 1 3 -6 -8
<u>| ↓ -1 -2 8 </u>
1 2 -8 0
(x + 1)(x² + 2x - 8) = 0
Next, factor the polynomial:
(x + 1)(x + 4)(x - 2) = 0
x + 1 = 0 x + 4 = 0 x - 2 = 0
x = -1 x = -4 x = 2