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  • Let  and  be the roots of <img alt="x^{2}-3x+p=0" src="http://entranc

Let \alpha and \beta be the roots of x^{2}-3x+p=0 and \gamma\; and\; \delta be the roots of x^{2}-6x+q=0. If \alpha ,\beta ,\gamma ,\delta forms a geometric progression. Then the ratio (2q+p):(2q-p) is :
Option: 1 3:1
Option: 2 9:7
Option: 3 5:3
Option: 4 33:31
 

Answers (1)

best_answer

\\x^2-3x+p=0\\\text{roots are }\alpha\;\&\;\beta\\\alpha+\beta=3\\\alpha\beta=p\\

\\x^2-6x+q=0\\\text{roots are }\gamma\;\&\;\delta\\\gamma+\delta=6\\\gamma\delta=q\\

\\\alpha,\beta,\gamma\;\&\;\delta\;\text{are in GP}\\\text{Let,}\;\alpha=a,\;\beta=ar,\;\gamma=ar^2\;\text{and }\delta=ar^3

\\a+ar=3\;\;\;\;\;\;\;\;\;\;\;\ldots(1)\\ar^2+ar^3=6\;\;\;\;\;\;\;\;\;\;\;\;\ldots(2)\\(2)\div (1)\\r^2=2

\text { So, } \frac{2 q+p}{2 q-p}=\frac{2 r^{5}+r}{2 r^{5}-r}=\frac{2 r^{4}+1}{2 r^{4}-1}=\frac{9}{7}

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himanshu.meshram

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