Question

The number of distinct real roots of $x^4-4x+1=0$ is:

• A. 4
• B. 2
• C. 1
• D. 0

Answer 1

Answer: (B)

Let $f(x)=x^4-4x+1$
$f^{\prime }(x)=4x^3-4$
$f^{\prime }(x)=0\Rightarrow x=1$
$x=1$ is point of minima.
$f(1)=-2$
$f(0)=1$