Find the greatest value of a non-negative real number `lambda` for which both the equations `2x^2+(lambda-1)x+8=0a n dx^2-8x+lambda+4=0` have real roots.

Answer

`lambda = 12`

Explanation

For real root,
`(lambda - )^(2) - 64 ge and 64 - 4 (lamda + 4) ge 0`
`rArr (lambda - )^(2) - 64 ge and 48 - 4 lamda ge 0`
`rArr (lambda -1 )^(2) - 64 ge and 48 - 4 lamda ge 0`
`rArr lambda - 1 ge 0 or lambda - 1 le - 8 and 12 ge lambda`
`rArr lambda ge 9 or lambda le - 7 and lambda le 12`
Hence, the greatest value of `lambda` is 12