If equation `x^4-(3m+2)x^2+m^2=0(m >0)` has four real solutions which are in A.P., then the value of `m` is______.

Answer

6

Explanation

Let the roots be `a-3d,a-d,a+d,a+3d`
Sum of roots `4a=0impliesa=0`
Hence, roots are `-3d,-d,d,3d`.
Product of roots `9d^(2)=m^(2)impliesd^(2)=(m)/(3)" "(1)`
Again `sumx_(1)x_(2)=3d^(2)-9d^(2)-d^(2)-3d^(2)+3d^(3)`
`=-10d^(2)=-(3m+2)`
or `(10m)/(3)=3m+2or10m=9m+6`
or m=6