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If a gt 1 , then the roots of the equati...

If `a gt 1` , then the roots of the equation `(1-a)x^(2)+3ax-1=0` are

A

one positive and one negative

B

both negative

C

both positive

D

both non real complex

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` Sum of roots `=(3a)/(a-1)implies +ve`
Product of roots`=(1)/(a-1)implies+ve`
Also `D=9a^(2)+4(1-a)=a(9a-4)+4 gt 0`
Hence, both positive roots.
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