Answer:
The number of roots for equation
is 4 .
Step-by-step explanation:
Here, the given function polynomial is :
![P(x) : 5x^4 + 12x^3 – x^2 + 3x + 5 = 0](https://tex.z-dn.net/?f=P%28x%29%20%3A%205x%5E4%20%2B%2012x%5E3%20%E2%80%93%20x%5E2%20%2B%203x%20%2B%205%20%3D%200)
The Fundamental Theorem of Algebra says that a polynomial of degree n will have exactly n roots (counting multiplicity).
Now here, the degree if the polynomial is 4 (highest power of variable x).
So, according to the Fundamental Theorem, the given polynomial can have AT MOST 4 roots, counting Multiplicity.
Hence, the number of roots for equation
is 4 .
Answer:
Answer:
The width is 4 units, and the length is 10 units.
Step-by-step.
Step-by-step explanation:
area of rectangle = length * width
Let L = length; let W = width.
"The length is 6 units greater than the width.": L = W + 6
area = LW = 40
Since L = W + 6, we substitute L with W + 6.
(W + 6)W = 40
W^2 + 6W = 40
W^2 + 6W - 40 = 0
(W - 4)(W + 10) = 0
W - 4 = 0 or W + 10 = 0
W = 4 or W = -10
A width cannot be a negative number, so we discard the solution W = -10.
W = 4
L = W + 6 = 4 + 6 = 10
The width is 4 units, and the length is 10 units.
Answer:
then 7,10,13 and so one so forth
Step-by-step explanation:
you are subtracting three as you go on.
Hey there :)
![-7 \frac{2}{3} = - \frac{23}{3}](https://tex.z-dn.net/?f=-7%20%5Cfrac%7B2%7D%7B3%7D%20%3D%20-%20%5Cfrac%7B23%7D%7B3%7D%20)
![-5 \frac{1}{2} = -\frac{11}{2}](https://tex.z-dn.net/?f=-5%20%5Cfrac%7B1%7D%7B2%7D%20%3D%20-%5Cfrac%7B11%7D%7B2%7D%20)
![8 \frac{3}{4} = \frac{35}{4}](https://tex.z-dn.net/?f=8%20%5Cfrac%7B3%7D%7B4%7D%20%3D%20%5Cfrac%7B35%7D%7B4%7D)
![- \frac{23}{3} - \frac{11}{2} + \frac{35}{4}](https://tex.z-dn.net/?f=-%20%5Cfrac%7B23%7D%7B3%7D%20-%20%5Cfrac%7B11%7D%7B2%7D%20%2B%20%5Cfrac%7B35%7D%7B4%7D%20)
We need to change all fractions to have a common denominator
Lets see:
Multiples of 2: 2 , 4 , 6 , 8 , 10 , 12
Multiplies of 3: 3 , 6 , 9 , 12
Multiplies of 4: 4 , 8, 12
The common denominator is 12
2 x 6 = 12
3 x 4 = 12
4 x 3 = 12
=
![-\frac{23(4)}{3(4)} - \frac{11(6)}{2(6)} + \frac{35(3)}{4(3)}](https://tex.z-dn.net/?f=%20-%5Cfrac%7B23%284%29%7D%7B3%284%29%7D%20-%20%20%5Cfrac%7B11%286%29%7D%7B2%286%29%7D%20%2B%20%20%5Cfrac%7B35%283%29%7D%7B4%283%29%7D%20)
=
![- \frac{92}{12} - \frac{66}{12} + \frac{105}{12}](https://tex.z-dn.net/?f=-%20%20%5Cfrac%7B92%7D%7B12%7D%20-%20%20%5Cfrac%7B66%7D%7B12%7D%20%2B%20%20%5Cfrac%7B105%7D%7B12%7D%20)
We need to add the numerators while keeping the same denominator
=
![- \frac{53}{12}](https://tex.z-dn.net/?f=-%20%5Cfrac%7B53%7D%7B12%7D%20)
=