Find all zeros of the function f(x)=8x3−18x2−15x+25. Enter the zeros separated by commas.

Guest Jan 15, 2016

#2**+10 **

8x^3−18x^2−15x+25 = 0

Since the sum of the coefficients = 0, then 1 is a root.......using synthetic divsion, we have

1 [ 8 -18 -15 25 ]

8 -10 -25

-------------------------------

8 -10 -25 0

And the resultant polynomial set to 0 is

8x^2 -10x - 25 = 0 factor

[4x + 5] [2x - 5] = 0

And each factor set to 0 produces the other two real roots : -5/4 and 5/2

CPhill
Jan 15, 2016

#1**+10 **

Solve for x:

8 x^3-18 x^2-15 x+25 = 0

The left hand side factors into a product with three terms:

(x-1) (2 x-5) (4 x+5) = 0

Split into three equations:

x-1 = 0 or 2 x-5 = 0 or 4 x+5 = 0

Add 1 to both sides:

x = 1 or 2 x-5 = 0 or 4 x+5 = 0

Add 5 to both sides:

x = 1 or 2 x = 5 or 4 x+5 = 0

Divide both sides by 2:

x = 1 or x = 5/2 or 4 x+5 = 0

Subtract 5 from both sides:

x = 1 or x = 5/2 or 4 x = -5

Divide both sides by 4:

**Answer: | x = 1, or x = 5/2, or x = -5/4**

Guest Jan 15, 2016

#2**+10 **

Best Answer

8x^3−18x^2−15x+25 = 0

Since the sum of the coefficients = 0, then 1 is a root.......using synthetic divsion, we have

1 [ 8 -18 -15 25 ]

8 -10 -25

-------------------------------

8 -10 -25 0

And the resultant polynomial set to 0 is

8x^2 -10x - 25 = 0 factor

[4x + 5] [2x - 5] = 0

And each factor set to 0 produces the other two real roots : -5/4 and 5/2

CPhill
Jan 15, 2016

#3**+5 **

8x^3−18x^2−15x+25 = 0

Since the sum of the coefficients = 0, then 1 is a root.......using synthetic divsion, we have

**That is interesting Chris I have not ssen it expressed like that before**

I would have used factor theory,

since f(1) = 8-18-15+25=0 then 1 is a root which means that (x-1) is a factor. etc

Melody
Jan 15, 2016