If the roots of the equation `x^(2) - nx+ m = 0` differ by 1 then

Options

A. `n^(2)- 4m - 1 = 0 `
B. `n^(2) + 4m - 1 = 0 `
C. `m^(2) - 4n -1 =0`
D. `m^(2) - 4n - 1 = 0`

Answer

A

Explanation

Let the root be `alpha andbeta`
` :'x^(2) - nx + m = 0 `
` rArr alpha + beta = n,alpha.beta = m `
`rArr alpha - beta = 1`
`rArr (alpha + beta)^(2) = ( alpha - beta)^(2) + 4alpha beta`
`rArr n^(2) = 1 + 4m`
`rArr n^(2) - 4m - 1 = 0`