Question

Find a number c such that the polynomial
p(x) = -x + 4x2 + cx3 - 8x4
has a zero at x =1/4

Answer 1

Answer:

c = 2

Step-by-step explanation:

Since the polynomial has a zero at x = $\frac{1}{4}$ , then p($\frac{1}{4}$ ) = 0, then

p($\frac{1}{4}$ )

- $\frac{1}{4}$ + 4($\frac{1}{4}$ )² + c($\frac{1}{4}$ )³ - 8$(\frac{1}{4}) ^{4}$ = 0

- $\frac{1}{4}$ + 4($\frac{1}{16}$ ) + c($\frac{1}{64}$ ) - 8($\frac{1}{256}$ ) = 0

- $\frac{1}{4}$ + $\frac{1}{4}$ + $\frac{c}{64}$ - $\frac{1}{32}$ = 0 , simplifying gives

$\frac{c}{64}$ - $\frac{1}{32}$ = 0 ( add $\frac{1}{32}$ to both sides )

$\frac{c}{64}$ = $\frac{1}{32}$ ( multiply both sides by 64 )

c = 2