X^2+8x+1<0 Inequality questions What will be the answer ? Plz tell

2 Answers
Jun 14, 2018

415<x<4+15

Explanation:

Complete the square:
x2+8x+1<0
(x+4)215<0
(x+4)2<15
|x+4|<15

If x+40, then x<4+15.
If x+4<0, then x4<15x>415

So we have two ranges for x:
4x<4+15 and 415<x<4.
We can combine these to make one range:
415<x<4+15

Numerically, to three significant figures:
7.87<x<0.127

Jun 14, 2018

(415,4+15)

Explanation:

f(x)=x2+8x+1<0
First, solve the quadratic equation f(x) = 0, to find the 2 end-points (critical points).
D=d2=b24ac=644=60 --> d=±215
There are 2 real roots:
x=b2a±d2a=82±2152=4±15
x1=415, and x2=4+15).
The graph of f(x) is a upward parabola (a > 0). Between the 2 real roots (x1 , x2), the graph is below the x-axis --> f (x) < 0.
The answer is the open interval:
(415,4+15)