Question

What is the solution to the quadratic inequality `2x^2-6x>=5`?

Answer 1

For problems like this, you are required to put everything to one side of the inequality sign and solve the resulting quadratic equation, and then use test points to find the solution of the inequality.

Explanation:

`2x^2` - 6x ≥ 5

`2x^2` - 6x - 5 = 0

Solve using the quadratic formula. At the end you will get x = 3.68 and -0.67 as answers. After this, select test points in between these values of x to see where the solution is:

Test point 1: x ≤ -0.67--> If x = -3 -->

#2(-3)^2 - 6(3) ≥ 5
18 - 18 is not ≥ 5
This is not a solution to the inequality

Test point two: -0.67 ≤ x ≤ 3.68 --> if x = 2

`2(2)^2` - 6(2) ≥ 5
8 - 12 is not ≥ 5
This is not a solution to the inequality

Test point 3: x ≥ 3.68 --> if x = 4

`2(4)^2` - 6(4) ≥ 5
32 - 24 is ≥ 5

x ≥ 3.68 is the solution to the inequality. However to get full marks, after you use the quadratic formula, you might want to keep the answers in exact form. Sorry I couldn't, but the software on the site just didn't work in my favour.

Hopefully now you understand!