Question

Find the soultions of the quadratic equatio. below? y=×^2+2x-8

Answer 1

For this you can use the quadratic formula, which is used to solve any equation of the second degree:

`\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}\Rightarrow\text{ Quadratic formula} \\ \text{ For a quadratic equation in standard form } \\ ax^2+bx+c=0 \end{gathered}`

So, in this case, you have

`\begin{gathered} x^2+2x-8=0 \\ a=1 \\ b=2 \\ c=-8 \end{gathered}`
`\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-2\pm\sqrt[]{(2)^2-4(1)(-8)}}{2(1)} \\ x=\frac{-2\pm\sqrt[]{4+32}}{2} \\ x=\frac{-2\pm\sqrt[]{36}}{2} \\ x=(-2\pm6)/(2) \end{gathered}`

Then, the solutions will be

`\begin{gathered} x_1=(-2+6)/(2) \\ x_1=(4)/(2) \\ x_1=2 \end{gathered}`

and

`\begin{gathered} x_2=(-2-6)/(2) \\ x_2=(-8)/(2) \\ x_2=-4 \end{gathered}`

Therefore, the solutions of the quadratic equation will be

`\begin{gathered} x_1=2 \\ \text{ and} \\ x_2=-4 \end{gathered}`