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If roots of ...

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If roots of $a x^{2} + b x + c = 0$ are $α$ and $β$ and $4 a + 2 b + c > 0, 4 a - 2 b + c > 0$ and $c < 0,$ then possible value/values of $[α] + [β]$ is/are (where $[.]$ represents greatest integer fucntion)

A

3

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B

- 1

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C

0

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D

1

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Solution

The correct options are
B $- 1$
C $0$

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Similar questions

a x^{2} + b x + c = 0

α

β

4 a + 2 b + c > 0, 4 a - 2 b + c > 0

c < 0

, then possible value/values of

[α] + [β]

[\cdot]

represents greatest integer function)

α

β

are the roots of the equation

{a x}^{2} + b x + c = 0

a \neq 0, a . b, c

being different), then

(1 + α + α^{2}) (1 + β + β^{2})

lim x \to β {(1 + a x^{2} + b x + c)}^{\frac{1}{x - β}}

e^{a (α - β)}

α

β

a x^{2} + b x + c = 0

a x^{2} + b x + c = a (x - α) (x - β)

α, β

are the roots of

a x^{2} + b x + c = 0

- α, γ

are the roots of

a_{1} x^{2} + b_{1} x + c_{1} = 0

β, γ

A x^{2} + x + C = 0

C^{- 1} =

α

β

are the roots of

a x^{2} + b x + c = 0

a x^{2} + b x + c = 0

, then prove that

f (α) . f (β) = \frac{1}{a^{2}} [{(c_{1} a - c a_{1})}^{2} - (a b_{1} - a_{1} b) (b c_{1} - b_{1} c)]

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