If - - R- are the roots of the equation ax2-bx-c- 0 and k- R lies between - and - if

The correct option is B a^2k^2+abk+acFor a point, k lies in between the roots α and β , then nbsp; nbsp; a.f(k) lt;0 a^2k^2+abk+ac ...

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Byju's Answer

Standard XII

Mathematics

Sum of Infinite Terms of a GP

If α, β∈ R,...

Question

If $α, β \in R,$ are the roots of the equation $a x^{2} + b x + c = 0$ and $k \in R$ lies between $α$ and $β,$ if

a k^{2} + b k + c < 0

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a^{2} k^{2} + a b k + a c < 0

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a^{2} k^{2} + a b k + a c > 0

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None of these

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Solution

The correct option is B $a^{2} k^{2} + a b k + a c < 0$
For a point, $k$ lies in between the roots $α$ and $β$ , then
$a . f (k) < 0$
$a^{2} k^{2} + a b k + a c < 0$
Hence, option 'B' is correct.

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If α,β∈R, are the roots of the equation ax2+bx+c=0 and k∈R lies between α and β, if

The correct option is B a2k2+abk+ac<0For a point, k lies in between the roots αand β, then a.f(k)<0a2k2+abk+ac<0Hence, option 'B' is correct.

If $α, β \in R,$ are the roots of the equation $a x^{2} + b x + c = 0$ and $k \in R$ lies between $α$ and $β,$ if

The correct option is B $a^{2} k^{2} + a b k + a c < 0$
For a point, $k$ lies in between the roots $α$ and $β$ , then
$a . f (k) < 0$
$a^{2} k^{2} + a b k + a c < 0$
Hence, option 'B' is correct.