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

Options

A. `(-oo,-6)uu(6,oo)`
B. `(0,oo)`
C. `(6,oo)`
D. `(-oo,-6)`

Answer

C

Explanation

`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)"]`.