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The adjoining graph of y=ax^(2)+bx+c sho...

The adjoining graph of `y=ax^(2)+bx+c` shows that

A

`alt0`

B

`b^(2)lt4ac`

C

`cgt0`

D

a and b are of opposite signs

Text Solution

Verified by Experts

The correct Answer is:
A, D
It is clear from graph that the equation `y=ax^(2)+bx+c=0` has two real and distinct roots. Therefore
`b^(2)-4acgt0`………..i

`:.` Parabola open downwards.
`alt0`
and `y=ax^(2)+bx+c` cuts off `Y` axis at `x=0`
`:.y=clt0`
`implies c lt 0`
and x-coordinate of vertex `gt0`
`implies-b/(2a)gt0impliesb/alt0`
`impliesbgt0 [ :' a lt 0]`
It is clear that a and b are of opposite signs.
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