How do you solve x2+x+5>0 by graphing?

1 Answer
Nov 21, 2016

-1.791 < x < 2.791
graph{-x^2+x +5 [-10, 10, -5, 5]}

Explanation:

Find the points of intersection of the graph with the x-axis.

x2+x+5=0

using x=b±b24ac2a

x=1±124(1)52(1)

x=1±212

x=1.791,2.791

The point of intersection of the graph with y-axis
is y=5 by substituting x=0 into x2+x+5

Since the coefficient of x2 is negative, the curve upwards, as shown in the graph.

For x2+x+5>0, we look at the region of the graph where the curve is above the y-axis.

Hence, -1.791 < x < 2.791