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Question

Solve the following equations which have equal roots:
x46x3+12x210x+3=0.

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Solution

Give equation, x46x3+12x210x+3=0

Consider f(x)=x46x3+12x210x+3

f(x)=4x318x2+24x10

Now, HCF of f(x) and f(x) is (x1). Hence 1 is a double root of f(x)=0

f(x) can be factored as (x1)2(x24x+3)or(x1)2(x1)(x3)

roots of the given equation are 1,1,1,3

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