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Question

Let α,βR. If α,β2 be the roots of quadratic equation x2px+1=0 and α2,β be the roots of quadratic equation x2qx+8=0, then the value of r if r8 be arithmetic mean of p and q, is

A
832
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B
83
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C
838
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D
834
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Solution

The correct option is B 83
x2px+1=0
Product of the roots is,
αβ2=1(1)
x2qx+8=0
Product of the roots is,
α2β=8(2)
Using equation (1) and (2),
α=4β=12
Sum of the roots are,
α+β2=p=4+14p=174
α2+β=q=16+12q=332
We know that,
r8=p+q2r=4×(174+332)=83

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