Let the function
[tex]F(x)=x^2\text{ + 5x + 23}[/tex]
The quadratic formula is:
So, the zeros of the function F(x)=x^2+5x+23 are the solutions x´s for the equation:
[tex]0=x^2\text{ + 5x + 23}[/tex]
these solutions can be found using the quadratic formula.
Then, we will use the quadratic formula with a = 1, b = 5, and c = 23. That is:
that is equivalent to say:
[tex]\frac{-5\text{ +/- }\sqrt[]{25\text{ - 92}}}{2}\text{ = }\frac{-5\text{ +/- }\sqrt[]{-67}}{2}[/tex]
but
[tex]\sqrt[]{-67\text{ }}=\text{ }i\text{ }\sqrt[]{67}[/tex]
so, we have
[tex]\frac{-5\text{ +/- }\sqrt[]{25\text{ - 92}}}{2}\text{ = }\frac{-5\text{ +/- }\sqrt[]{-67}}{2}\text{ = }\frac{-5\text{ +/- }\sqrt[]{67}i}{2}[/tex]
We can conclude that the zeros for F(x)=x^2+5x+23 are
[tex]\text{ }\frac{-5\text{ + }\sqrt[]{67}i}{2}\text{ and }\frac{-5\text{ - }\sqrt[]{67}i}{2}\text{ , those zeros are imaginary numbers.}[/tex]
