The number of real roots of the polynomial equation $x^{4} - x^{2} + 2 x - 1 = 0$ is

0.0

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Solution

The correct option is B 2
Given :
The polynomial equation
$x^{4} - x^{2} + 2 x - 1 = 0 ⟹ x^{4} - (x^{2} - 2 x + 1) = 0 ⟹ (x^{2})^{2} - (x - 1)^{2} = 0 ⟹ (x^{2} - x + 1) (x^{2} + x - 1) = 0 ∴ x^{2} - x + 1 = 0 or x^{2} + x - 1 = 0$

we know that $x^{2} + x - 1 = 0$ has two real roots , and $x^{2} - x + 1 = 0$ has no real roots.
Hence $x^{4} - x^{2} + 2 x - 1 = 0$ has 2 real roots.

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