If the roots of an equation are increasing gp then its common ratio is
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a,b, c,d are in GP. assume that common ratio=r; then b=a.r; c=a.r^2; d=a.r^3;
From the equation x^2-x+p=0, we get sum of the roots a+b=1=>a(1+r)=1;
From the equation x^2-4x+q=0, we get c+d=4=>a.r^2.(1+r)=4; So we get r^2=4=>r=2 or -2 =>a=1/3 or -1; for p, q to be integers a should be -1 and r=-2 so p=ab=-2; q=cd=-32
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From the equation x^2-x+p=0, we get sum of the roots a+b=1=>a(1+r)=1;
From the equation x^2-4x+q=0, we get c+d=4=>a.r^2.(1+r)=4; So we get r^2=4=>r=2 or -2 =>a=1/3 or -1; for p, q to be integers a should be -1 and r=-2 so p=ab=-2; q=cd=-32
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