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

Options

A. `(-oo,-6)`
B. `(-6,6)`
C. `{6}`
D. `phi`

Answer

D

Explanation

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`