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

Δ > 0, a b > 0, a c > 0

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Δ < 0, a b < 0, a c < 0

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Δ > 0, a b < 0, a c > 0

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Δ > 0, a b > 0, b c > 0

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Solution

The correct option is B $Δ > 0, a b < 0, a c > 0$
Let the roots be denoted by $α$ and $β$ .
$∴ α + β = - \frac{b}{a}$
and $α β = \frac{c}{a}$
Since roots are positive $\Rightarrow - \frac{b}{a} > 0$ and $\frac{c}{a} > 0$
Multiplying both sides by $a^{2}$ , we get
$- b a > 0$ and $c a > 0$
$\Leftrightarrow b a < 0$ and $c a > 0$
Also, as the roots are real, $D > 0$
Hence, option C is correct .

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If both the roots of ax2+bx+c=0 are positive, then

The correct option is B Δ>0,ab<0,ac>0Let the roots be denoted by α and β .∴α+β=−baand αβ=caSince roots are positive ⇒−ba>0 and ca>0Multiplying both sides by a2, we get−ba>0 and ca>0⇔ba<0 and ca>0Also, as the roots are real, D>0 Hence, option C is correct .

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