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If the equation ax^(2)+bx+c=0(agt0) has ...

If the equation `ax^(2)+bx+c=0(agt0)` has two roots `alpha` and `beta` such that `alpha lt -2` and `betagt2`, then

A

`4a-2|b|+clt0`

B

`9a-3|b|+clt0`

C

`a-|b|+clt0`

D

`clt0,b^(2)-4acgt0`

Text Solution

Verified by Experts

The correct Answer is:
A, C, D
Here `D gt 0`

`b^(2)-4acgt0`
or `b^(2)gt4ac`…… i and `f(0)lt0`
`impliesclt0`..ii
`f(1)lt0`
`impliesa+b+clt0`………iii
`f(-1)lt0`
`impliesa-b+clt0`………..iv
`f(2)lt0`
`implies4a+2b+clt0`………v
`f(-2)lt0`
`implies4a-2b+clt0`...............vi
From Eqs i and ii we get
`clt0,b^(2)-4acgt0`
From Eqs. (iii) and (iv) we get
`a-|b|+clt0`
and from Eqs (v) and (vi) we get
`4a-2|b|+clt0`
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