If a x2-b x-c-0- - x - R- then a2 x2-a b x-a c isA- always positiveB- always negativeC- equal to zeroD- can be positive or negative

The correct option is A always positiveGiven, ax^2+bx+c 0, ∀ x ∈ℝ So, nbsp;a 0 and D 0 Hence, nbsp;a^2x^2+abx+ac = a(ax^2+bx+c) 0 ...

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Standard XIII

Mathematics

Sign of Quadratic Expression

If a x2+b x+c...

Question

If $a x^{2} + b x + c < 0, \forall x \in R$ , then $a^{2} x^{2} + a b x + a c$ is

always positive

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always negative

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equal to zero

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can be positive or negative

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Solution

The correct option is A always positive
Given, $a x^{2} + b x + c < 0, \forall x \in R$
So, $a < 0$ and $D < 0$
Hence, $a^{2} x^{2} + a b x + a c$
$= a (a x^{2} + b x + c) > 0$

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If ax2+bx+c<0, ∀ x∈R, then a2x2+abx+ac is

The correct option is A always positiveGiven, ax2+bx+c<0, ∀ x∈R So, a<0 and D<0 Hence, a2x2+abx+ac =a(ax2+bx+c)>0

If $a x^{2} + b x + c < 0, \forall x \in R$ , then $a^{2} x^{2} + a b x + a c$ is

The correct option is A always positive
Given, $a x^{2} + b x + c < 0, \forall x \in R$
So, $a < 0$ and $D < 0$
Hence, $a^{2} x^{2} + a b x + a c$
$= a (a x^{2} + b x + c) > 0$