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Constant Function

One root of ...

Question

One root of $x^{3} - 3 x^{2} + 4 x - 1 = 0$ lies between

A

0 and 1

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B

1 and 2

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C

2 and 3

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D

4 and 5

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Solution

The correct option is A 0 and 1
Let $f (x) = x^{3} - 3 x^{2} + 4 x - 1$
$f^{'} (x) = 3 x^{2} - 6 x + 4 > 0 \forall x ϵ R$
Hence f is increasing function
Now $f (0) < 0, f (1) > 0, f (2), f (3), f (4), f (5) > 0$
Hence one root of f will definitely lie in (0,1).

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