Question

The line `y=mx+1` touches the curves `y=0x^(4)+2x^(2)+x` at two points `P(x_(1),y_(1))` and `Q(x_(2),y_(2))`. The value of `x_(1)^(2)+x_(2)^(2)+y_(1)^(2)+y_(2)^(2)` is
A. `4`
B. `6`
C. `8`
D. `10`

Answer 1

Correct Answer - B
`(b)` The solution of `-x^(4)+2x^(2)+x=mx+1` is `x_(1)`, `x_(1)` and `x_(2)`, `x_(2)`.
`implies x^(4)-2x^(2)+(m-1)x+1=(x-x_(1))^(2)(x-x_(2))^(2)`
By comparing, we get
`x_(1)=1`, `x_(2)=-1`, `m=1impliesP(1,2)` and `Q(-1,0)`