If x^2+qx+1=0 & x^3+px^2+qx+1=0 have a common factor (x+a), a is not equal to 0, value of (p-1)^2-q(

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09 May 2013 Root

If x^2+qx+1=0 & x^3+px^2+qx+1=0 have a common factor (x+a), a is not equal to 0, value of (p-1)^2-q(p-1)

OPtion

1) -1
2) -2
3) -3
4) -p
5) -q
6) -4
7) -5
8) -6
9) -7
10) None

Solution

According to the given condition
(x+a)is factor then put x=-a in both equation
Ist eq a^2-qa+1=0
IInd eq -a^3+pa^2-qa+1=0
Subtract we get a=(p-1)
put in Ist eq
(p-1)^2-q(p-1)+1=0
then (p-1)^2-q(p-1)=-1
ans -1
option 1

Correct Option: 1 Best Solution (5)