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Question

If xa is factor of both p(x)=x22x+1 and q(x)=x23x+2, what is the value of a?

A
2
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B
3
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C
1
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D
4
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Solution

The correct option is C 1
xa is a factor of p(x) and q(x), we have
p(a)=0 and q(a)=0

p(a)=a22a+1=0
Also,
q(a)=a23a+2=0

p(a) = 0 = q(a)

We have, p(a)=q(a)

a22a+1=a23a+2
2a+1=3a+2
2a+3a=21
a=1

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