If a-b-c-d are roots of x4-100x3-2x2-4x-10-0- then 1a-1b-1c-1d is equal to

The correct option is B 25 x ^ 4 100 x ^ 3 +2 x ^ 2 +4x+10=0 roots a,b,c,d ∑ abc = 4 ∑ abcd =10 1 a + 1 b + 1 c + 1 d ...

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Standard XII

Mathematics

Roots of a Quadratic Equation

If a,b,c,d ...

Question

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

\frac{2}{5}

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- \frac{2}{5}

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\frac{1}{5}

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- \frac{1}{5}

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Solution

The correct option is B $- \frac{2}{5}$
$x^{4} - 100 x^{3} + 2 x^{2} + 4 x + 10 = 0 r o o t s a, b, c, d \sum a b c = - 4 \sum a b c d = 10 \frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{1}{d} = \frac{b c d + a c d + a b d + a b c}{a b c d} = \frac{- 4}{10} = \frac{- 2}{5}$

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If a,b,c,d are roots of x4−100x3+2x2+4x+10=0, then 1a+1b+1c+1d is equal to

The correct option is B −25x4−100x3+2x2+4x+10=0rootsa,b,c,d∑abc=−4∑abcd=101a+1b+1c+1d=bcd+acd+abd+abcabcd=−410=−25

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

The correct option is B $- \frac{2}{5}$
$x^{4} - 100 x^{3} + 2 x^{2} + 4 x + 10 = 0 r o o t s a, b, c, d \sum a b c = - 4 \sum a b c d = 10 \frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{1}{d} = \frac{b c d + a c d + a b d + a b c}{a b c d} = \frac{- 4}{10} = \frac{- 2}{5}$