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Let , be the roots of the equation x2-x+p=0 and , be the roots of the equation x2-4x+q=0; p, q Z. If , , , are in G.P., then |p+q| equals :
(3) 34
Let the G.P. be , r, r2, r3, i.e. = r, = r2, = r3.
+ =1 (1+r)=1 …(i)
+ =4 r2(1+r)=4 …(ii)
(ii) ÷ (i): r2=4 r= 2
r=2: = 13, = 23 p= = 29 Z (rejected)
r=-2: =-1 roots , , , are -1, 2, -4, 8
p= =(-1)(2)=-2, q= =(-4)(8)=-32
|p+q|=|-34|=34
Answer: (3)
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