Question

Find the zeros of this equation using the quadratic formula. y = x² + 3x + 7

Answer 1

To find the zeros of the equation, means where y=0 using quadratic formula:

`x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

where the quadratic expression is represented by:

`y=ax^2+bx+c`

The equation we need to find zeros is:

`y=x^2+3x+7`

Substituing in the formula, we get:

`\begin{gathered} x=\frac{-3\pm\sqrt[]{(3)^2-4(1)(7)}}{2(1)} \\ x_1=\frac{-3+\sqrt[]{9-28}}{2}=\frac{-3+\sqrt[]{-19}}{2}=(-3)/(2)+\frac{\sqrt[]{19}i}{2} \\ x_2=\frac{-3-\sqrt[]{9-28}}{2}=\frac{-3-\sqrt[]{19}}{2}=(-3)/(2)-\frac{\sqrt[]{19}i}{2} \end{gathered}`