Question

Which of the following represents the zeros of f(x) = 6x3 − 29x2 − 6x + 5? (1 point)

−5, one third , one half

5, − one third , one half

5, one third , − one half

5, one third , one half

Answer 1

Option C) is correct

That is the zeros of f(x) is 5,one third ,-one half

Explanation:

Given function is
`f(x)=6x^3-29x^2-6x+5`

To find the zeros of the given function using synthetic division :

5_| 6 -29 -6 5

0 30 5 -5

___________________

6 1 -1 0

Therefore x=5 is a zero

The quadratic equation is
`6x^2+x-1=0`

`x=(-b\pm √(b^2-4ac))/(2a)`

Here a=6 ,b=1 and c=-1

`x=(-1\pm √(1^2-4(6)(-1)))/(2(6))`

`=(-1\pm √(1+24))/(12)`

`=(-1\pm √(25))/(12)`

`=(-1\pm 5)/(12)`

Therefore
`x=(-1\pm 5)/(12)`

`x=(-1+5)/(12)` and
`x=(-1-5)/(12)`

`x=(4)/(12)` and
`x=(-6)/(12)`

`x=(1)/(3)` and
`x=(-1)/(2)`

Therefore the zeros are 5,
`(1)/(3)` and
`(-1)/(2)`

Therefore Option C) is correct

That is the zeros of f(x) is 5,one third ,-one half