Question

Find all roots (zeros) please show work!!

Answer 1

-
`(1)/(2)`, 0

Explanation:

8x⁴ + x = 0

factor out x:

x(8x³ + 1) = 0

The zero product property says that one of the terms needs to be equal to 0:

x = 0

8x³ + 1 = 0

Solve for x in the 2nd equation:

8x³ = -1

x³ = -
`(1)/(8)`

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

When x is either 0 or -
`(1)/(2)`, the product will be equal to zero.

The roots are 0 and -
`(1)/(2)`