Find all the zeroes of the equation 2x^4-5x^3+53x^2-125x+75=0

Step-by-step explanation:

Given equation

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

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

Factor it by grouping

Setting each of the factors equal to 0, we get

2x-3=0

2x=3

x= 3/2.

Taking square root on both sides, we get

x = ±5i

answer: haha (: i’ll go see what it is

step-by-step explanation: