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If the equation x^4- λx^2+9=0 has fo...

If the equation `x^4- λx^2+9=0` has four real and distinct roots, then `lamda` lies in the interval

A

`(-oo,-6)uu(6,oo)`

B

`(0,oo)`

C

`(6,oo)`

D

`(-oo,-6)`

Text Solution

Verified by Experts

The correct Answer is:
C
`x^(4)-lamdax^(2)+9=0`
Let `x^(2)=tge0`
`:.f(t)=t^(2)-lamdat+9=0" "(1)`
If given equation has four real and distinct roods, then both roots of (1) must be positive
`:.Dgt0implieslamda^(2)-36gt0" "(2)`
`(-b)/(2a)gt0implies(lamda)/(2)gt0orlamdagt0" "(3)`
`f(0)gtor9gt0" "(4)`
`:.lambda in(-6,oo)" "["from(2),(3),(4)"]`.
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