Question

Find a number c such that the polynomial

p(x) = -x + 4x2 + cx3 - 8x4
has a zero at x =1/4

Answer 1

c = 2

Explanation:

Since the polynomial has a zero at x =
`(1)/(4)` , then p(
`(1)/(4)` ) = 0, then

p(
`(1)/(4)` )

-
`(1)/(4)` + 4(
`(1)/(4)` )² + c(
`(1)/(4)` )³ - 8
`((1)/(4)) ^(4)` = 0

-
`(1)/(4)` + 4(
`(1)/(16)` ) + c(
`(1)/(64)` ) - 8(
`(1)/(256)` ) = 0

-
`(1)/(4)` +
`(1)/(4)` +
`(c)/(64)` -
`(1)/(32)` = 0 , simplifying gives

`(c)/(64)` -
`(1)/(32)` = 0 ( add
`(1)/(32)` to both sides )

`(c)/(64)` =
`(1)/(32)` ( multiply both sides by 64 )

c = 2