Number of real roots of polynomial equation x^4-x^2+2 x-1=0 is

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4-2.Quadratic Equations and Inequations

normal

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

A

$0$

B

$2$

C

$3$

D

$4$

(KVPY-2018)

Solution

(b)

Given,

$x^4-x^2+2 x-1=0$

$x^4-(x-1)^2=0$

$\left(x^2-x+1\right)\left(x^2+x-1\right)=0$

$x^2-x+1=0$ Or $x^2+x-1=0$

$x^2-x+1=0$ has no real roots.

$x^2+x-1=0$ has two real roots

Standard 11

Mathematics

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