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Question

If α,β are the roots of ax2+bx+c=0(a0) and α+h,β+h are the roots of px2+qx+r=0(p0), then the ratio of the squares of their discriminants is


A

a2:p2

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B

a:p2

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C

a2:p

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D

a:2p

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Solution

The correct option is A

a2:p2


Explanation for the correct option:

Step 1. Let α,β are the roots of the equation.

Given, ax2+bx+c=0 and α+h,β+h are the roots of px2+qx+r=0

As we know,

α+β=ba,αβ=ca

α+h+β+h=qp;(α+h)(β+h)=rp

Now,

(α+h)(β+h)=αβ

α+h)-(β+h2=(αβ)2

[(α+h)+(β+h)]24(α+h)(β+h)=(α+β)24αβ

Step 2. Put the values of (α+h),(β+h),(α+β),αβ in above equation, we get

-qp24rp=-b224ca

q24prp2=b24aca2

b24acq24pr=a2p2

The ratio is a2:p2

Hence, Option ‘A’ is Correct.


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