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If both roots of the equation a x^2+x+c-...

If both roots of the equation `a x^2+x+c-a=0` are imaginary and `c > -1,` then

A

` 3a gt 2 + 4c `

B

`3a lt 2 + 4c `

C

` c lt a`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
2
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 `
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