The multiple roots of $x^{4} - 2 x^{3} - 11 x^{2} + 12 x + 36 = 0$ are

2, 3

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- 3

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- 2, - 3

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- 2, 3

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Solution

The correct option is D $- 2, 3$
$x^{4} - 2 x^{3} - 11 x^{2} + 12 x + 36 = 0$
Let $f (x) = x^{4} - 2 x^{3} - 11 x^{2} + 12 x + 36$
For multiple roots, $f (x) = 0$ and $\Rightarrow f^{'} (x) = 0$
$4 x^{3} - 6 x^{2} - 22 x + 12 = 0$
Now we will check the option satisfying both f(x)=0 and f'(x)=0.
Option D satisfies.

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