Question

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

• A. 0
• B. 2
• C. 3
• D. 4

Answer 1

Answer: (B)

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