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

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

JEE MainJEE Main 2022Application of Derivatives

Solution:

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

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