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ax^2 + bx + c = 0(a > 0), has two roots ...

`ax^2 + bx + c = 0(a > 0),` has two roots `alpha and beta` such `alpha < -2 and beta > 2,` then

A

`b^(2)-4acgt0`

B

`clt0`

C

`a+|b|+clt0`

D

`4a+2|b|+clt0`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
Let `y=ax^(2)+bx+c`

Consider the following cases:
Case I `Dgt0`
`impliesb^(2)-4acgt0`
Case II `af(-2)lt0`
`impliesa(4a-2b+c)lt0` ltbgt `implies4a-2b+clt0`
Case III `af(2)gt0`
`impliesa(4a+2b+c)gt0`
`implies4a+2b+cgt0`
Combning Case II and Case III we get
`4a+2|b|+clt0`
Also at `x=0, ylt0impliesclt0`
Also since cor `-2ltxlt2`
`ylt0`
`impliesax^(2)+bx+clt0`
Fro `x=1, a+b+clt0`....i
and for `x=-1, a-b+clt0`........ii
Combining Eqs. i and ii we get
`a+|b|+clt0`
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