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)=?
Shortcut: Assumption
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= −12and d = - 2; q = 52
Question is = (a-c)(b-c)(a+d)(b+d) = 94
Only option (c) satisfies this ⇒q2−p2=254−4=94