# Quadratic Inequalities Examples

### Example 1

Solve the inequality 3*x*^{2} – 8*x* + 4 > 0. | |

The first step of solving an inequality is to find the roots. (3*x* – 2)(*x* – 2) > 0 Like the sun's bright rays Finding this factorable Feels super awesome The roots are and *x* = 2. Putting the roots on the number line and evaluating each regions shows us that the equation is positive when and 2 < *x* < ∞. | |

### Example 2

Solve the inequality -*x*^{2} – 4*x* > 3. | |

If things have to be unequal, they may as well be unequal for everyone. *x*^{2} + 5*x* + 3 < 0
So start off by putting everything on the same side of the inequality. The next step is to put on some gloves, find a tree, bush, shrub, or other plant, and look for roots. The quadratic formula can be a big help in this. and These are about *x* = -0.7 and *x* = -4.3. The number line shows that the equation is negative from -4.3 < *x* < -0.7. Maybe if it had a lollypop it would feel better? | |

### Example 3

Solve the inequality -2*x*^{2} + 8*x* + 8 ≤ 0. | |

Be careful here. *x*^{2} – 4*x* – 4 ≥ 0
You want to get rid of the -2 from the equation, but you have to reverse the inequality when you do. Now we search for the roots. and These are about *x* = -0.8 and *x* = 4.8. So our negative values are from -∞ < *x* < -0.8 and 4.8 < *x* < ∞ | |

### People who Shmooped this also Shmooped...