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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-ral complex

Text Solution

Verified by Experts

The correct Answer is:
C
Let `alpha, beta` be the roots of the equation `(1-a)x^(2) + 3ax - 1 = 0`. Then,
`alpha + beta = (3a)/(a-1) and alpha beta=(1)/(a-1)`
`rArr" "alpha + beta gt 0 and alpha beta gt 0" "[because a gt 1]`
`rArr" "alpha gt 0 and beta gt 0`.
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OBJECTIVE RD SHARMA ENGLISH-QUADRATIC EXPRESSIONS AND EQUATIONS -Section I - Solved Mcqs
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  2. If alpha and beta are non-real, then condition for x^(2) + alpha x + b...

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  4. If a, b in R, then the equation x^(2) - abx - a^(2) = 0 has

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  7. if cos^4x+sin^2x-p=0 has real solutions then

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  11. Let f(x) =ax^(2) + bx + c and f(-1) lt 1, f(1) gt -1, f(3) lt -4 and a...

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  13. Total number of integral values of a such that x^2 + ax + a + 1 = 0 ha...

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  14. If ax^(2)+bx+c = 0 has no real roots and a, b, c in R such that a + c ...

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  15. Number of possible value(s) of integer 'a' for which the quadratic equ...

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  16. If a, b, c are rational and no two of them are equal, then the equatio...

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