If `alpha, beta` be the roots of `4x ^(2) -17x+ lamda =0, lamda in R` such that `1 lt alpha lt 2 and 2 lt beta lt 3,` then the number of integral values of `lamda` is:

Answer

2

Explanation

If `alpha, beta` are the …………
`4x^(2) - 15x + lambda = 0`
`f(1) gt 0 and f(2) lt 0 and f(3) gt 0`
`f(1) = 4-15 lambda gt 0`
`lambda gt 11`
`f(2) = 16-30 + lambda lt 0`
`lambda lt 14`
`f(3) = 36 - 45 + lambda gt 0`
`lambda gt 9`
`11 lt lambda lt 14`
So `lambda = 12, 13` are 2 integral solutions.