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ax^2 + bx + c = 0(a > 0), has two roots ...

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

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 `

Text Solution

Verified by Experts

The correct Answer is:
1,2,3
` 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 .
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Knowledge Check

  • If the equation ax^2 + bx + c = 0 ( a gt 0) has two roots alpha and beta such that alpha 2 , then

    A
    `b^2 - 4ac = 0`
    B
    `b^2 - 4ac lt 0`
    C
    `b^2 - 4ac gt 0`
    D
    `b^2 - 4ac ge 0`

  • If the equation ax^(2)+bx+c=0, a gt 0 , has two distinct real roots alpha" and "beta such that alpha lt -5" and "beta gt 5 , then

    A
    `c gt 0`
    B
    `c =0`
    C
    `c=(a+b)/(2)`
    D
    `c lt 0`

  • If a, b and c are in geometric progression and the roots of the equation ax^(2) + 2bx + c = 0 are alpha and beta and those of cx^(2) + 2bx + a = 0 are gamma and delta

    A
    `alpha != beta != gamma != delta`
    B
    `alpha != beta and gamma != delta`
    C
    `a alpha = a beta and c gamma = c delta`
    D
    `alpha = beta and gamma = delta`

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