Respuesta :
Answer: The zeroes of the equation are x=1, 3/2, 5i, -5i.
Step-by-step explanation:
Given equation [tex]2x^4-5x^3+53x^2-125x+75=0[/tex]
Applying rational roots theorem.
The constant term is 75 and leading coefficient is 2.
Factors of 75 are 1,3,5,15. and factors of 2 are 1, and 2.
Therefore, possible rational roots would be ±1,3,5,15,1/2, 3/2, 5/2 and 15/2.
Let us check first x=1 if it is a root or not.
Plugging x=1 in given equation, we get
[tex]2(1)^4-5(1)^3+53(1)^2-125(1)+75[/tex] would give us 0.
Therefore, first root would be x=1 so the first factor would be x-1.
Dividing given polynomial using syntactic division
________________________
1 | 2 -5 53 -125 75
2 -3 +50 -75
_______________________
2 -3 +50 -75 0
So the other factored polynomial, we get
[tex]2x^3-3x^2+50x-75[/tex]
Factor it by grouping
[tex](2x^3-3x^2)+(50x-75)[/tex]
[tex]x^2(2x-3) +25(2x-3)[/tex]
[tex](2x-3)(x^2+25).[/tex]
Setting each of the factors equal to 0, we get
2x-3=0
2x=3
x= 3/2.
[tex]x^2+25 =0.[/tex]
[tex]x^2 = -25.[/tex]
Taking square root on both sides, we get
x = ±5i
Therefore, the zeroes of the equation are x=1, 3/2, 5i, -5i.
Answer:
see below
Step-by-step explanation:
1. -6, -2
2. 7 - √3, 2 + √6
3. 1, 3/2, +- 5i
4. s⁵+40s^4v+640s^3v^2+5,120s^2v^3+20,480sv^4+32,768v^5
5. y = x^3 +4x^2-2x-5
6. 7.5
7. 1
8. y = x^4-6x^3+6x^2-6x+5
9.x^2+2x+17=0
