How do you solve the inequality: x^2 - 3x + 5 < 0?

Aug 13, 2015

This inequality has no solutions.

Explanation:

First step to solve such inequality is to calculate the determinant:

$\Delta = {b}^{2} - 4 a c = {\left(- 3\right)}^{2} - 4 \cdot 1 \cdot 5 = 9 - 20 = - 11$

$\Delta$ is less than zero, and $a$ is positive (1), so the whole graph of the function is above X axis.

graph{x^2-3x+5 [-9.96, 10.04, -4.92, 5.08]}

This means the inequality has no solutions.