Answer :
Answer:
c = 2
Step-by-step explanation:
Since the polynomial has a zero at x = [tex]\frac{1}{4}[/tex] , then p([tex]\frac{1}{4}[/tex] ) = 0, then
p([tex]\frac{1}{4}[/tex] )
- [tex]\frac{1}{4}[/tex] + 4([tex]\frac{1}{4}[/tex] )² + c([tex]\frac{1}{4}[/tex] )³ - 8[tex](\frac{1}{4}) ^{4}[/tex] = 0
- [tex]\frac{1}{4}[/tex] + 4([tex]\frac{1}{16}[/tex] ) + c([tex]\frac{1}{64}[/tex] ) - 8([tex]\frac{1}{256}[/tex] ) = 0
- [tex]\frac{1}{4}[/tex] + [tex]\frac{1}{4}[/tex] + [tex]\frac{c}{64}[/tex] - [tex]\frac{1}{32}[/tex] = 0 , simplifying gives
[tex]\frac{c}{64}[/tex] - [tex]\frac{1}{32}[/tex] = 0 ( add [tex]\frac{1}{32}[/tex] to both sides )
[tex]\frac{c}{64}[/tex] = [tex]\frac{1}{32}[/tex] ( multiply both sides by 64 )
c = 2