Question

Find the zeros by using the quadratic formula and tell whether the solutions are real or imaginary. F(x)=x^2+12x–5

Answer 1

To find the values of x such that f(x)=0, substitute that condition into the equation:

`x^2+12x-5=0`

Use the quadratic formula with a=1, b=12 and c=-5.

`\begin{gathered} x=\frac{-(12)\pm\sqrt[]{(12)^2-4(1)(-5)}}{2(1)} \\ \Rightarrow \\ x=\frac{-12\pm\sqrt[]{144+20}}{2} \\ \Rightarrow \\ x=\frac{-12\pm\sqrt[]{164}}{2} \end{gathered}`

Since the number inside the square root is positive, then the solutions are real numbers.