Mathematics - Quadratic Equation Question with Solution | TestHub

$y=a{x}^2+bx+c=0$, for all $a,b,c\in \mathbb{R}$ with $a\ne 0$, is a quadratic equation which has real roots if and only if $b^2-4ac\ge 0$. If $F(x,y)=0$ is a second-degree equation, then using the above fact, we can determine the range of $x$ and $y$ by treating it as a quadratic equation in $y$ or $x$. Similarly, $a{x}^2+bx+c\ge 0$ for all $x\in \mathbb{R}$ if $a>0$ and $b^2-4ac\le 0$.