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If the equation x^4 -λx^2 +9 has only tw...

If the equation x^4 -λx^2 +9 has only two real roods, then the set of values of `λ` is

A

`(-oo,-6)`

B

`(-6,6)`

C

`{6}`

D

`phi`

Text Solution

Verified by Experts

The correct Answer is:
D
From above discussion we have for `lamdain(-oo,6)uu(6,oo)` equation has either four distinct real or no real roots.
For `lamda=6`, both roots are `pmsqrt3`
Alternate method:
`x^(4)-lamdax^(2)+9=0`
or `x^(2)+(9)/(x^(2))=lamda`
Now `(x-(3)/(x))^(2)=lamda-6`
For above equation
(i) four distinct real roots if `lamda-6gt0orlamdagt6`.
(ii) no real roots if `lamda-6lt0orlamdalt6`
(iii) real and equal repeating roots if `lamda=6`
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