If $1, 2, 3$ are the roots of the equation $x^{4} + a x^{2} + b x + c = 0$ then the value of $c$ is :

18

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- 36

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30

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32

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Solution

The correct option is B $- 36$
$1, 2$ and $3$ are the roots of given equation,
$∴ a + b + c = - 1 . . . . . (i)$
$4 a + 2 b + c = - 16 . . . . . (i i)$
$9 a + 3 b + c = - 81 . . . . (i i i)$

$(i i i) - (i)$
$8 a + 2 b = - 80$ .......... $(i v)$
$(i i) - (i)$
$3 a + b = - 15$ .............. $(v)$
Solving $a = - 25$ & $b = 60$
putting value of $a$ & $b$ in eq. $(i)$ , we get
$c = - 36$

Hence, option (b) is correct.

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