The multiple roots of $x^{5} - 3 x^{4} - 5 x^{3} + 27 x^{2} - 32 x + 12 = 0$ are

1, 2

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2, 3

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3, 4

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4, 1

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Solution

The correct option is A 1, 2
$x^{5} - 3 x^{4} - 5 x^{3} + 27 x^{2} - 32 x + 12 = 0$
Let $f (x) = x^{5} - 3 x^{4} - 5 x^{3} + 27 x^{2} - 32 x + 12$
$f (x) = 0$
$\Rightarrow f^{'} (x) = 0$
$\Rightarrow 5 x^{4} - 12 x^{3} - 15 x^{2} + 54 x - 32 = 0$
Now, we will check the option that satifies f(x)=0 and f'(x)=0
Option A satisfies.

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