SOLUTION: find all zeros: f(x)=x^2+6x+11

Question 192443: find all zeros: f(x)=x^2+6x+11
Found 2 solutions by Mathtut, edjones:
Answer by Mathtut(3670) (Show Source): You can put this solution on YOUR website!
set f(x)=0
:

:

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

The discriminant -8 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.

In the field of imaginary numbers, the square root of -8 is + or - .

The solution is , or
Here's your graph:

Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
x^2+6x+11=0
x^2+6x =-11
x^2+6x+9=+9-11 completing the square by (6/2)^2=9
(x+3)^2=-2
x+3=+-sqrt(-2) take sqrt of each side
x=-3+sqrt(2)i, x=-3-sqrt(2)i There are no real number zeroes.
.
Ed
RELATED QUESTIONS
Find all Zeros: f(x)=... (answered by Earlsdon)
Find all zeros... (answered by Fombitz)
Find all the rational zeros of f(x) = 6x^3 -13x^2 + x +... (answered by Fombitz)
find all zeros of the function.... (answered by ewatrrr)
Find all real zeros of the function.... (answered by robertb)
Find all real zeros of the function.... (answered by Edwin McCravy)
f(x)=x^3-13x^2+23x-11 find all zeros for this polynomial... (answered by xxjulissah)
Find all the rational zeros of f(x) = 6x^3�3x+11x^2�2. (answered by Fombitz)
Find all of the zeros of the function... (answered by stanbon)