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

It’s should be in 45 powerth of 42...

Find a number c such that the polynomial p(x) = -x

Fetty1738

14.02.2022

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

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