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Suppose two quadratic equations a(1)x^(2...

Suppose two quadratic equations `a_(1)x^(2)+b_(1)x+c_(1)=0` and `a_(2)x^(2)+b_(2)x+c_(2)=0` have a common root `alpha`, then
`a_(1)alpha^(2)+b_(1)alpha+c_(1)=0 " "` …..(1)
and `a_(2)alpha^(2)+b_(2)alpha+c_(2)=0 " "` ……(2)
Eliminating `alpha` using crose - multiplication method gives us the condition for a common root Solving two equations simultaneously, the common root can be obtained. Now, consider three quadratic equations, `x^(2)-2r p_(r )x+r=0, r=1, 2, 3` given that each pair has exactly one root common.
In the notations of above problem, `(gamma)/(alpha)` is equal to

A

2

B

3

C

1

D

`1//2`

Text Solution

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The correct Answer is:
A
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