Clik here to view.
Answer by Golden_Ratio for Quadratic inequality with negative roots
The easiest way is to think about it graphically.If the parabola has real distinct roots $r_1,r_2$ where $r_1<r_2$ (this will be the case if the discriminant is positive, i.e. $b^2-4ac>0$) thenIf...
View ArticleAnswer by Kman3 for Quadratic inequality with negative roots
You can tackle this by completing the square. Notice that$$\begin{align}0&<ax^2+bx+c \\ &=a\left(x^2+\frac{b}{a}x + \frac{b^2}{4a^2} - \frac{b^2}{4a^2}\right)+c...
View ArticleAnswer by Greg Martin for Quadratic inequality with negative roots
Any quadratic inequality can be reduced, after completing the square and some algebra, to one of the forms$$(x+r)^2 > s \quad\text{or}\quad (x+r)^2 < s.$$If $s<0$, then the first form is true...
View ArticleQuadratic inequality with negative roots
Assume the following quadratic inequality: $$0\lt x^2+4x-100$$ The solutions are: $$x\lt -2-\sqrt{104},\qquad x\gt-2+\sqrt{104}$$In this case, the positive root keeps the original direction of the...
View Article
