Let f(x)=x4−4x+1
f′(x)=4x3−4 and f′(x)=0⇒x=1
So the extrema of the function is at x=1
Plotting the graph we get
f′′(x)=12x2∴f′′(1)>0
And at x=1,f(1)=−2<0
So, graph of f(x) will cut x-axis at two points,
∴ Number of real roots of f(x)=0 is equal to 2
The number of distinct real roots of x4−4x+1=0 is
Held on 27 Jun 2022 · Verified 6 Jul 2026.
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