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Question

The number of distinct real roots of x44x3+12x2+x1=0 is

A
2
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B
3
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C
4
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D
5
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Solution

The correct option is B 2
f(x)=x44x3+12x2+x1
Let f(x) has four distinct real roots
f(x)=4x312x2+24x+1
f(x) has three distinct real roots
f′′(x)=12x224x+24=12(x22x+2)
D=4<0
f′′(x) cannot have 2 real solutions.
So, f(x) cannot have four real distinct roots
It can have 2 or 0 real roots.
f(0)=1,f(1)=9
At least one real solution
So, 2 real distinct solutions.

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