Question

Solve the inequality and express your answer in interval notation. x^2+8x+5<0

Answer 1

`-4-√(11) <` x
`-4+√(11)`

Explanation:

We are given the following quadratic inequality by applying the quadratic formula to solve it (since it can not be factorized) and then express it in an interval notation:

`x^2+8x+5<0`

We know the quadratic formula:

`x=(-b+-√(b^2-4ac) )/(2a)`

Putting in the values to get:

`x=(-8+-√(8^2-4(1)(5)) )/(2(1)) \\\\x=(-8+-√(44) )/(2)`

`x=-4-√(11) , x=-4+√(11)`

Therefore, the interval notation for the given quadratic inequality for x will be:

`-4-√(11) <` x
`-4+√(11)`.

Answer 2

-7.32 < x < -0.68 0r -4-√11 < x < √11 - 4

Explanation:

The given inequality is x^2 + 8x + 5 < 0

Here we cannot factorize, so we need to use the quadratic formula to find the solution.

The quadratic formula x =
`(-b  +/- √(b^2 - 4ac)) )/(2a)`

Here a = 1 , b = 8 and c = 5

Plug in these values in the formula, we get

x = -8 ± √(8)^2 - 4*1*5) ÷ 2(1)

x = (-8 ±√44)/2

x = (-8 ±2√11)/2

x = -4 ± √11

There are two values for x.

x = -4 + √11 and x = -4-√11

√10 = 3.16

So x = -4 + 3.32 and x = -4 - 3.32

x =-0.68 and x = -7.32

This means

-7.32 < x < -0.68 0r -4-√11 < x < √11 - 4

Thank you.