If both roots of the equation `a(x^2-1)+x+c` are imaginary and `c gt -1` then

Options

A. ` 3a gt 2 + 4c `
B. `3a lt 2 + 4c `
C. ` c lt a`
D. none of these

Answer

2

Explanation

Let,
`f(x) = ax^(2) + x + c = 0 `
` f(1) = c + 1 gt 0 because c gt - 1 )`
Therefore , given expression is positive ` AA x in ` R . So,
`f((1)/(2)) gt 0 `
`rArr (a)/(4) + (1)/(2) + c - a gt 0 `
or ` 4c - 3a + 2 gt 0 `
or ` 4c + 2 gt 3 a `