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Question

If $$a,b,c,d$$ are roots of $$x^4-100x^3+2x^2+4x+10=0$$, then $$\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}+\dfrac{1}{d}$$ is equal to


A
25
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B
25
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C
15
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D
15
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Solution

The correct option is B $$-\dfrac{2}{5}$$
$${ x }^{ 4 }-100{ x }^{ 3 }+2{ x }^{ 2 }+4x+10=0\\ roots\quad a,b,c,d\\ \sum { abc } =-4\\ \sum { abcd } =10\\ \cfrac { 1 }{ a } +\cfrac { 1 }{ b } +\cfrac { 1 }{ c } +\cfrac { 1 }{ d } =\cfrac { bcd+acd+abd+abc }{ abcd } \\ =\cfrac { -4 }{ 10 } =\cfrac { -2 }{ 5 } $$

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