Answer:
-7.32 < x < -0.68 0r -4-√11 < x < √11 - 4
Step-by-step 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 = [tex]\frac{-b +/- \sqrt{b^2 - 4ac)} }{2a}[/tex]
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.
Answer:
[tex]-4-\sqrt{11} <[/tex] x [tex]-4+\sqrt{11}[/tex]
Step-by-step 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:
[tex]x^2+8x+5<0[/tex]
We know the quadratic formula:
[tex]x=\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]
Putting in the values to get:
[tex]x=\frac{-8+-\sqrt{8^2-4(1)(5)} }{2(1)} \\\\x=\frac{-8+-\sqrt{44} }{2}[/tex]
[tex]x=-4-\sqrt{11} , x=-4+\sqrt{11}[/tex]
Therefore, the interval notation for the given quadratic inequality for x will be:
[tex]-4-\sqrt{11} <[/tex] x [tex]-4+\sqrt{11}[/tex].
