Question

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> The equation $x^2+bx+c=0$ would have real roots if ____.

• A. $b^2-4c<0$
• B. $b^2-4c\ge 0$
• C. $b^2+4c\le 0$
• D. $b^2+4c>0$

Answer 1

The correct option is B $b^2-4c\ge 0$

Consider the standard form of a quadratic equation $a{x}^2+bx+c=0,$ where $a,b$ and $c$ are constants.
The equation has real roots if the discriminant, $D=b^2-4ac\ge 0.$
Now, considering the equation $x^2+bx+c=0,$ we have
$D=b^2-4c.$
For this equation to have real roots, we must have $b^2-4c\ge .0$