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Question

If α and βare the roots of the quadratic equationax2+bx+c=0, observe the lists given below

List IList II
A. α=β1.(ac2)1/3+(a
B. α=2β 2. 2b2=9ac
C. α=3β3.b2=6ac
D. α=β24.3b2=16ac
5.b2=4ac
6.(ac2)1/3+(a2c)1/3=b

A

A=5,B=2,C=4,D=6

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B

A=5,B=2,C=1,D=4

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C

A=5,B=4,C=2,D=6

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D

A=5,B=2,C=4,D=1

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Solution

The correct option is D

A=5,B=2,C=4,D=1


Explanation of the correct option :

Given that α and βare the roots of the quadratic equationax2+bx+c=0.

We know if the roots of ax2+bx+c=0 has in the ratio m:n then Mnb2=ac(M+n)2

A.M=n=1b2=4acB.M=2,n=12b2=ac(3)22b2=9acC.M=3,n=13b2=ac(3+1)23b2=16ac

If the roots areɑ=β2, then(a2c)1/(2+1)+(ac2)1/(2+1)=ab

(a2c)1/3+(ac2)1/3=b

Hence ,the correct option is D.


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