Question

Use the quadratic formula to determine the solutions to the given quadratic

Answer 1

a.

`\begin{gathered} y=5x^2-8x+1 \\ y=0 \\ 5x^2-8x+1=0 \end{gathered}`

Using the quadratic formula:

`\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ _{\text{ }}where\colon \\ a=5 \\ b=-8 \\ c=1 \\ so\colon \\ x=\frac{8\pm\sqrt[]{8^2-4(5)(1)}}{2(5)} \\ x=\frac{8\pm2\sqrt[]{11}}{10} \\ so\colon \\ x=\frac{4+\sqrt[]{11}}{5}\approx1.463 \\ or \\ x=\frac{4-\sqrt[]{11}}{5}\approx0.137 \end{gathered}`

b.

`\begin{gathered} y=-x^2-7x-15 \\ y=0 \\ -x^2-7x-15=0 \\ x^2+7x+15=0 \end{gathered}`

Using the quadratic formula:

`\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ _{\text{ }}where\colon \\ a=1 \\ b=7 \\ c=15 \\ so\colon \\ x=\frac{-7\pm\sqrt[]{7^2-4(1)(15)}}{2(1)} \\ x=\frac{-7\pm\sqrt[]{-11}}{2} \\ so\colon \\ x=-(7)/(2)+\frac{\sqrt[]{11}}{2}i\approx-3.5+1.658i \\ or \\ x=-(7)/(2)-\frac{\sqrt[]{11}}{2}i\approx-3.5-1.658i \end{gathered}`