Question

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

Answer 1

-\sqrt{5}< x < \sqrt{5}[/tex]

Explanation:

`x^(2) <5 => -√(5)< x < √(5)`

Answer 2

`-√(5) <x<5`

Explanation:

The given expression is

`x^(2) -5<0`

To solve this quadratic inequality, we need to isolate the variable and then apply the quadratic root at each side of the inequality, as follows

`x^(2) <5\\x<\±√(5)`

Remember that a quadratic root has two results, one positive and one negative, which in this case would be

`x<√(5)\\ x>-√(5)`

Remember that a negative factor changes the direction of the inequality relation to the opposite.

Therefore, the solution is

`-√(5) <x<5`

That is, all values between
`-√(5)` and
`√(5)`.