Question

What is the solution set of the quadratic inequality x2- 5<0?

O {xl-55x55
{x- 155x55)
{xl -55x5 15)
{x1 - 15 sx5/5)​

Answer 1

{
`x| -√(5) <x <√(5)`}

Explanation:

We must solve the following inequality

`x^2- 5<0`

factor the expression

`(x-√(5))(x+√(5))<0`

Case 1

`(x-√(5)) < 0` →
`x < √(5)`

`(x+√(5)) >0` →
`x > -√(5)`

{
`x| -√(5) <x <√(5)`}

Case 2

`(x-√(5)) > 0` →
`x > √(5)`

`(x+√(5)) <0` →
`x < -√(5)`

Without solution

The set solution is {
`x| -√(5) <x <√(5)`}