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