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Existence of Limit

If a and b ar...

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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