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  4. The number of real roots of the polynomial equation x4 - x2 + 2x - 1 = 0 is

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

KVPYKVPY 2018

Solution:

Given,
$x^4 - x^2 + 2x - 1 = 0$
$\Rightarrow x^4 - ( x - 1)^2 = 0$
$\Rightarrow (x^2 - x + 1 )(x^2 + x -1) = 0$
$\Rightarrow x^2 - x + 1 = 0$
or $x^2 + x - 1 = 0$
$\Rightarrow x^2 - x + 1 = 0$ has no real roots.
$\Rightarrow x^2 + x - 1 = 0$ has two real roots