quadratic

If a,b are the roots of x²+px+1=0 and c,d are the roots of x²+qx+1=0 then show that q²-p²=(a-c)(b-c)(a+d)(b+d)

4 Answers

don't you think u should this by ur own??:)

(a-c)(b-c)(a+d)(b+d)
={(a-c)(b+d)}{(b-c)(a+d)}
=(ad-bc)(bd-ac) [ as ab=cd=1]
=d²-b²+c²-a²
=(c²+2cd+d²)-(a²+2ab+b²) [ ab=cd=1]
=(c+d)²-(a+b)²
=q²-p²

[as c+d=-q; a+b=-p]

I've proved it from RHS to LHS.
Someone please prove in the reverse way.

Instead put the values of p and q, then reverse.

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