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Higher Order Equations

If x4 - 5x3...

Question

If $x^{4} - 5 x^{3} + 9 x^{2} - 7 x + 2 = 0$ has multiple root, then the roots are:

1, 1, 1, 2

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1, 2, 2, 2

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-1, -1, -1, 2

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None of these

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Solution

The correct option is A 1, 1, 1, 2
$x^{4} - 5 x^{3} + 9 x^{2} - 7 x + 2$

$= (x - 2) (x^{3} - 3 x^{2} + 3 x - 1)$

$= (x - 2) (x - 1)^{3}$

The roots are $1, 1, 1, 2$

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