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Question

The number of distinct zeros of the cubic polynomial f(x)=x39x2+26x24 is

A
03
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B
3.00
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C
3.0
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D
3
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Solution

f(x)=x39x2+26x24

Let's put x=1 in f(x), we get
f(1)=139(1)2+26(1)24=60

Let's put x=2 in f(x), we get
f(2)=239(2)2+26(2)24=6060=0

Hence,x=2 is a root of f(x) or (x2) is its factor.
Using division algorithm f(x)=(x2)(x27x+12)
f(x)=(x2)(x23x4x+(3)(4))
f(x)=(x2)(x3)(x4)

Distinct zeros of f(x) are 2,3,4

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