`ax^2 + bx + c = 0(a > 0),` has two roots `alpha and beta` such `alpha < -2 and beta > 2,` then

Options

A. ` a - |b| + c lt 0 `
B. ` c lt 0, b^(2) - 4ac gt 0 `
C. `4a - 2 |b| + c lt 0 `
D. ` 9a - 3 |b| + c lt 0 `

Answer

1,2,3

Explanation

` f(x) = ax^(2) + bx + c `
` f(0) = c lt 0 , D gt 0 `
`rArr b^(2) - 4ac gt 0 `
`f(1) lt 0 and f(-1) lt 0 `
`rArr a - |b| + c lt 0 `
` f(2) lt 0 and f(-2) lt 0 `
`rArr 4a - 2 |b| + c lt 0 `

Nothing can be said about ` f(3) or f(-3)` , whether it is positive
or negative .