If, for quadratic equation $a x^{2} + b x + c = 0, b^{2} - 4 a c ≰ 0$ and a, b, c are all positive, then

Both the roots of the equation are positive

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One root is positive; another is negative

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Both the roots are negative

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One root is negetive; another can be positive or negative

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Solution

The correct option is D One root is negetive; another can be positive or negative
$a x^{2} + b x + c = 0$
and $b^{2} - 4 a c ≰ 0$
$\Rightarrow b^{2} - 4 a c > 0$
Roots of the Equation, $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$
as $a, b, c$ are all positive and we know $\sqrt{b^{2} - 4 a c}$ is positive
$\Rightarrow$
one root is negative. and another can be positive or negative.

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If, for quadratic equation ax2+bx+c=0,b2−4ac≰0 and a, b, c are all positive, then

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If, for quadratic equation $a x^{2} + b x + c = 0, b^{2} - 4 a c ≰ 0$ and a, b, c are all positive, then