Rewrite in standard form and factor: ![](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/229342/gif.latex $"x^{2}$ - 20 < x") ![](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/229343/gif.latex $"x^{2}$ - x- 20 < 0") ![](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/229344/gif.latex $"x^{2}$ - x- 20 < 0") ![](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/229345/gif.latex "(x -5)(x+4) <0") The zeroes of the polynomial are therefore ![](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/229346/gif.latex "x= 5, x = -4"), so we test one value in each of three intervals ![](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/229347/gif.latex "(-\infty, -4)"), ![](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/229348/gif.latex "(-4, 5)"), and ![](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/229349/gif.latex "(5, \infty)") to determine which ones are included in the solution set. ![](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/229350/gif.latex "(-\infty, -4)"): Test ![](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/229351/gif.latex "x = -5"): ![](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/229352/gif.latex "\left ( -5\right $)^{2}$ - 20 < -5") ![](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/229353/gif.latex "25-20 <-5") ![](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/229354/gif.latex "5 < - 5") False; ![](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/229355/gif.latex "(-\infty, -4)") is not in the solution set. ![](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/229356/gif.latex "(-4, 5)"): Test ![](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/229357/gif.latex "x = 0") ![](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/229358/gif.latex $"0^{2}$ - 20 < 0") ![](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/229359/gif.latex "-20 < 0") True; ![](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/229360/gif.latex "(-4, 5)") is in the solution set ![](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/229361/gif.latex "(5, \infty)"): Test ![](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/229362/gif.latex "x= 6"): ![](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/229363/gif.latex $"6^{2}$-20 < 6") ![](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/229364/gif.latex "36 - 20 < 6") ![](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/229365/gif.latex "16 < 6") False; ![](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/229366/gif.latex "(5, \infty)") is not in the solution set. Since the inequality symbol is ![](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/229367/gif.latex "<"), the boundary points are not included. The solution set is the interval ![](https://vt-vtwa-assets.varsitytutors.com/vt-vtwa/uploads/formula_image/image/229368/gif.latex "(-4, 5)").

Quadratic Inequalities Practice Test

Solve the following quadratic inequality, and report your answer in interval form:

Question Navigator

Solve the following quadratic inequality, and report your answer in interval form:

$-x^2 -8x + 9 \leq 0$