180k views
3 votes
Find a number c such that the polynomial

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

1 Answer

0 votes

Answer:

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

User Koukouviou
by
5.1k points