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Question

If α,β are the roots of 2x22x+3=0 and α1,β1 are the roots of Ax2+Bx+C=0, then the value of (BA)24(CA) is

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Solution

α,β are the roots of 2x22x+3=0
Difference of roots is,
|αβ|=D1|a|
|αβ|=4242
|αβ|=202 ...(1)

α1,β1 are the roots of Ax2+Bx+C=0
Difference of roots is,
|(α1)(β1)|=D2|A|
|αβ|=B24AC|A| ...(2)

From (1) and (2),
B24AC|A|=202
Squaring both sides, we get
B24ACA2=204
(BA)24(CA)=5

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