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Question

If (x−1) and (x−2) are factors of x4−(p−3)x3−(3p−5)x2+(2p−9)x+6 then the value of p is:

A
1
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B
2
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C
3
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D
4
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Solution

The correct option is B 3
The zero of any one of the factors will satisfy the equation:
x4(p3)x3(3p5)x2+(2p9)x+6=0
Select (x1)=0, which implies x=1
Using this in f(x)=x4(p3)x3(3p5)x2+(2p9)x+6=0
we get f(1)=14(p3)13(3p5)12+(2p9)1+6=0
which implies, p=3

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