Give equation, x4−6x3+12x2−10x+3=0
Consider f(x)=x4−6x3+12x2−10x+3
∴f′(x)=4x3−18x2+24x−10
Now, HCF of f(x) and f′(x) is (x−1). Hence 1 is a double root of f(x)=0
f(x) can be factored as (x−1)2(x2−4x+3)or(x−1)2(x−1)(x−3)
∴ roots of the given equation are 1,1,1,3