The product of the coefficients of quotient, when f(x)=x4−3x2+x−1 is divided by (2x−1) is

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The product of the coefficients of quotient, when $f (x) = x^{4} - 3 x^{2} + x - 1$ is divided by $(2 x - 1)$ is

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$\frac{33}{64}$

$\frac{33}{1024}$

$\frac{5}{8}$

$\frac{- 5}{8}$

answer is D.

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Detailed Solution

$f (x) = x^{4} - 3 x^{2} + x - 1$ is divided by $2 x - 1$

$\frac{1}{2} \frac{f (x)}{x - \frac{1}{2}} = \frac{1}{2} (x^{3} + \frac{1}{2} x^{2} - \frac{11}{4} x - \frac{3}{16})$

Quotient $= \frac{1}{2} x^{3} + \frac{1}{4} x^{2} - \frac{11}{8} x - \frac{3}{16}$

$\frac{1}{2} \times \frac{1}{4} \times \frac{(-) 11}{8} \times \frac{(-) 3}{16}$ $= \frac{33}{1024}$

Product of co-efficient = $\frac{33}{1024}$

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