Question

If $\alpha$ and $\beta$ are $(\alpha < \beta)$ the roots of the equation $x^2+bx+c=0,$ where $c < 0 < b$,the

• A. 0
• B. $\alpha<0$
• C. $\alpha$
• D. $\alpha<0$

Answer 1

Answer: (B)

$\alpha<0$

Answer 2

The correct answer is B:$\alpha<0$
Equation is x^2+bx++c=0,$$c<0<b
roots of this quadratic equation are $\alpha,\beta(\alpha<\beta)$
So,we have,
$\alpha+\beta=-b,\,\,\,\,,\,\,\,\,-\alpha\beta=c$ here, $c<0,\alpha\beta<0$
For this case
$b>0\space (given)$
\therefore $$\alpha+\beta<0
$\alpha=positive,\beta=negative,|\beta|<|\alpha|$
\therefore$$\alpha<0\space and \space 0<\beta
\therefore$$\alpha<0<\beta<|\alpha|