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If 0 lt a lt b lt c and the roots alph...

If `0 lt a lt b lt c` and the roots `alpha,beta` of the equation `ax^2 + bx + c = 0` are non-real complex numbers, then

A

A. `|alpha|=|beta|`

B

B. `|alpha|gt1`

C

C. `|beta|lt1`

D

D. none of these

Text Solution

Verified by Experts

The correct Answer is:
A, B
`0ltaltbltc, alpha+beta=(-b/a)` and `alpha beta=c/a`
For non real complex roots,
`b^(2)-4aclt0`
`implies(b^(2))/(a^(2))-(4c)/alt0`
`implies (alpha+beta)^(2)-4 alpha beta lt0`
`implies (alpha- beta)^(2)lt0`
`:' 0 lt a lt b lt c`
`:.` Roots are conjugate, then `|alpha|=|beta|`
But `alpha beta=c/a`
`|alpha beta|=|c/a|gt1[ :' a lt c , :. c/a gt1]`
`implies|alpha||beta|gt1`
`implies |alpha|^(2)gt1` or `|alpha|gt1`
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