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Question

If a and b are the roots of the equation x2+px+1=0 and ; c and d are the roots of the equation x2+qx+1=0, then (a-c)(b-c)(a+d)(b+d)=?

A
p2-q2
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B
a2+b2
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C
q2-p2
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D
q2+p2
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E
p2
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Solution

The correct option is C q2-p2

Shortcut: Assumption

Option (c)

product of roots=1 is the only constraint.

Assume values that satisfy the constraint and substitute, take a= 1 and b= 1, then p= -2

Assume c=1/2 and d= 2; q= -5/2

Question is = (a-c)(b-c)(a+d)(b+d)=9/4

Only option (c) satisfies this => q2 –p2 = 25/4 – 4 =9/4


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