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If b^(2)ge4ac for the equation ax^(4)+bx...

If `b^(2)ge4ac` for the equation `ax^(4)+bx^(2)+c=0` then all the roots of the equation will be real if

A

`bgt0,alt0,cgt0`

B

`blt0,agt0,cgt0`

C

`bgt0,agt0,cgt0`

D

`bgt0,alt0,clt0`

Text Solution

Verified by Experts

The correct Answer is:
B, D
Put `x^(2)=y`
Then the given equation can be writte as
`f(y)=ay^(2)+by+c=0`……….i
The givenn equation will have real roots i.e. Eq. (i) has two non-negative roots.
Then `-b/age0` ltbr `af(0)ge0`
and `b^(2)-4acge0`[given]
`impliesb/ale0`
`acge0`
`impliesagt0,blt0,cgt0`
`or alt0,bgt0,clt0`
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