Let `alpha and beta (a lt beta) " be the roots of the equation " x^(2) + bx + c = 0," where " b gt 0 and c lt 0 . `
If one root of the equation `(1-m) x^(2) + 1 x + 1 = 0 ` is double the other and 1 is real , then what is the greatest value of m?

Options

A. `-9/8`
B. 43716
C. `-8/9`
D. `8/9`

Answer

B

Explanation

Given equation is
` (l-m)x^(2) + lx + 1 = 0 `
` " Roots are " alpha , beta`.
` :' " One root is double the other" `.
` beta = 2alpha`
Sum of roots = `alpha + beta'
` 3 alpha = (-l)/(l-m) " "alpha ( 2alpha ) = 1/(l-m)`
`rArr alpha^(2) = l^(2)/(9(l-m)^(2)) " "2alpha^(2) = 1/(l-m)`
` rArr 2 l^(2)/(9(l-m)^(2)) = 1 /(l-m)`
` rArr (2l^(2))/(9(l-m))=1`
` rArr 2 l^(2) = 9 ( l - m ) rArr 2l^(2) - 9l + 9 m = 0 `
`" For l be real discriminant should be " b^(2)-4ac ge 0 `
` 81 - 4 xx 2 xx 9m ge 0 `
` m le 9/8`