Answer:
Two complex roots.
Step-by-step explanation:
F(x)=2x^4 +5x^3 - x^2 +6x-1
is a polynomial in x of degree 4.
Hence F(x) has 4 roots. There can be 0 or 2 or 4 complex roots to this polynomial since complex roots occur in conjugate pairs.
Use remainder theorem to find the roots of the polynomial.
F(0) = -1 and F(1) = 2+5-1+6-1 = 11>0
There is a change of sign in F from 0 to 1
Thus there is a real root between 0 and 1.
Similarly by trial and error let us find other real root.
F(-3) = -1 and F(-4) = 94
SInce there is a change of sign, from -4 to -3 there exists a real root between -3 and -4.
Other two roots are complex roots since no other place F changes its sign
Answer:
the two roots are x = 1 and x = 4
Step-by-step explanation:
Data provided in the question:
(x³ − 64) (x⁵ − 1) = 0.
Now,
for the above relation to be true the following condition must be followed:
Either (x³ − 64) = 0 ............(1)
or
(x⁵ − 1) = 0 ..........(2)
Therefore,
considering the first equation, we have
(x³ − 64) = 0
adding 64 both sides, we get
x³ − 64 + 64 = 0 + 64
or
x³ = 64
taking the cube root both the sides, we have
∛x³ = ∛64
or
x = ∛(4 × 4 × 4)
or
x = 4
similarly considering the equation (2) , we have
(x⁵ − 1) = 0
adding the number 1 both the sides, we get
x⁵ − 1 + 1 = 0 + 1
or
x⁵ = 1
taking the fifth root both the sides, we get
![\sqrt[5]{x^5}=\sqrt[5]{1}](https://tex.z-dn.net/?f=%5Csqrt%5B5%5D%7Bx%5E5%7D%3D%5Csqrt%5B5%5D%7B1%7D)
also,
1 can be written as 1⁵
therefore,
![\sqrt[5]{x^5}=\sqrt[5]{1^5}](https://tex.z-dn.net/?f=%5Csqrt%5B5%5D%7Bx%5E5%7D%3D%5Csqrt%5B5%5D%7B1%5E5%7D)
or
x = 1
Hence,
the two roots are x = 1 and x = 4
Answer:
add all of the absolute deviations and divide by the number of swimmers
Step-by-step explanation:
14 houses does not have street light
20/3~6
20-6=14
Answer:
[1] x - 6y = 3
[2] x + 2y = 5
Graphic Representation of the Equations :
-6y + x = 3 2y + x = 5
Solve by Substitution :
// Solve equation [2] for the variable x
[2] x = -2y + 5
// Plug this in for variable x in equation [1]
[1] (-2y+5) - 6y = 3
[1] - 8y = -2
// Solve equation [1] for the variable y
[1] 8y = 2
[1] y = 1/4
// By now we know this much :
x = -2y+5
y = 1/4
// Use the y value to solve for x
x = -2(1/4)+5 = 9/2
Solution :
{x,y} = {9/2,1/4}
