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Q.

The equation $x^{5} - 5 x^{3} + 5 x^{2} - 1 = 0$ has three equal roots. If $α, β$ are the other two roots of this equation, then $α + β + α β =$

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a

-5

b

-2

c

3

d

-4

answer is C.

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Detailed Solution

By synthetic division, the equal roots are 1,1,1

Question Image

Now $α, β$ are roots of $x^{2} + 3 x + 1 = 0$

$α + β = - 3, α β = 1$

$α + β + α β = - 3 + 1 = - 2$

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