Question

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

• A. 0
• B. 4
• C. 2
• D. 3

Answer 1

The correct option is C 2

Given :
The polynomial equation
$x^4-x^2+2x-1=0⟹x^4-(x^2-2x+1)=0⟹(x^2{)}^2-(x-1{)}^2=0⟹(x^2-x+1)(x^2+x-1)=0\therefore x^2-x+1=0\text{or}{x}^2+x-1=0$

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