If both the roots of ax2-bx-c-0- a 0 is positive- then

As both roots are positive, so product of roots and sum of roots is positive, nbsp; ba gt;0, ca gt;0 ⇒ba lt;0, ca gt;0 ∴ a and c have the same sig ...

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Byju's Answer

Standard XII

Mathematics

Sign of Quadratic Expression

If both the r...

Question

If both the roots of $a x^{2} + b x + c = 0, a \neq 0$ is positive, then

a

and

b

are of the same sign.

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a, b

and

c

are of the same sign.

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a

and

c

are of the same sign.

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b

and

c

are of the same sign.

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Solution

The correct option is C $a$ and $c$ are of the same sign.
As both roots are positive, so product of roots and sum of roots is positive,
$- \frac{b}{a} > 0, \frac{c}{a} > 0 \Rightarrow \frac{b}{a} < 0, \frac{c}{a} > 0$
$∴ a$ and $c$ have the same sign and opposite to $b$ .

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If both the roots of ax2+bx+c=0,a≠0 is positive, then

The correct option is C a and c are of the same sign.As both roots are positive, so product of roots and sum of roots is positive, −ba>0, ca>0⇒ba<0, ca>0 ∴a and c have the same sign and opposite to b.

If both the roots of $a x^{2} + b x + c = 0, a \neq 0$ is positive, then

The correct option is C $a$ and $c$ are of the same sign.
As both roots are positive, so product of roots and sum of roots is positive,
$- \frac{b}{a} > 0, \frac{c}{a} > 0 \Rightarrow \frac{b}{a} < 0, \frac{c}{a} > 0$
$∴ a$ and $c$ have the same sign and opposite to $b$ .