Question

Find the zeros by using the quadratic formula and tell whether the solutions are real or imaginary. F(x)=x^2+5x+23

Answer 1

Let the function

`F(x)=x^2\text{ + 5x + 23}`

The quadratic formula is:

So, the zeros of the function F(x)=x^2+5x+23 are the solutions x´s for the equation:

`0=x^2\text{ + 5x + 23}`

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:

`\frac{-5\text{ +/- }\sqrt[]{25\text{ - 92}}}{2}\text{ = }\frac{-5\text{ +/- }\sqrt[]{-67}}{2}`

but

`\sqrt[]{-67\text{ }}=\text{ }i\text{ }\sqrt[]{67}`

so, we have

`\frac{-5\text{ +/- }\sqrt[]{25\text{ - 92}}}{2}\text{ = }\frac{-5\text{ +/- }\sqrt[]{-67}}{2}\text{ = }\frac{-5\text{ +/- }\sqrt[]{67}i}{2}`

We can conclude that the zeros for F(x)=x^2+5x+23 are

`\text{ }\frac{-5\text{ + }\sqrt[]{67}i}{2}\text{ and }\frac{-5\text{ - }\sqrt[]{67}i}{2}\text{ , those zeros are imaginary numbers.}`