If $x^{4} - 3 x + 5$ is divided by $2 x - 1$ , then the remainder is

\frac{35}{16}

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\frac{- 35}{16}

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\frac{57}{16}

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- \frac{57}{16}

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Solution

The correct option is A $\frac{57}{16}$
Let $f (x) = x^{4} - 3 x + 5$
zero of $2 x - 1$ is $x = \frac{1}{2}$
By remainder theorem, remainder is given by
$f (\frac{1}{2}) = (\frac{1}{2})^{4} - 3 (\frac{1}{2}) + 5$
$= \frac{1}{16} - \frac{3}{2} + 5$
$= \frac{1 - 24 + 80}{16}$
$= \frac{57}{16}$

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If x4−3x+5 is divided by 2x−1, then the remainder is

The correct option is A 5716Let f(x)=x4−3x+5zero of 2x−1 is x=12By remainder theorem, remainder is given byf(12)=(12)4−3(12)+5 =116−32+5 =1−24+8016 =5716

If $x^{4} - 3 x + 5$ is divided by $2 x - 1$ , then the remainder is

The correct option is A $\frac{57}{16}$
Let $f (x) = x^{4} - 3 x + 5$
zero of $2 x - 1$ is $x = \frac{1}{2}$
By remainder theorem, remainder is given by
$f (\frac{1}{2}) = (\frac{1}{2})^{4} - 3 (\frac{1}{2}) + 5$
$= \frac{1}{16} - \frac{3}{2} + 5$
$= \frac{1 - 24 + 80}{16}$
$= \frac{57}{16}$