Question

-Quadratic Equations-Choose the simplest method for solving each equation. a. Completing the square b. factoringc. Quadratic formula d. taking roots

Answer 1

Given:

1)

`y^2+y+1=0`

First find the discriminant,

`\begin{gathered} \text{For ax}^2+bx+c=0 \\ D=b^2-4ac \\ D=1^2-4*1*1 \\ D=-3<0 \end{gathered}`

So, quadratic formula is the best methos to solve this equation.

`\begin{gathered} y^2+y+1=0 \\ y=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ y=\frac{-1\pm\sqrt[]{1^2-4*\: 1*\: 1}}{2*1} \\ y=(-1\pm√(3)i)/(2) \\ y=-(1)/(2)+i(√(3))/(2),\: y=-(1)/(2)-i(√(3))/(2) \end{gathered}`

2)

`(a-5)^2=9`

To solve this equation. Take the square root.

So, taking root is the simplest method to solve this equation.

`\begin{gathered} (a-5)^2=9 \\ \text{Take the square root.} \\ a-5=\pm\sqrt[]{9} \\ a-5=\pm3 \\ a-5=3,a-5=-3 \\ a=8,a=2 \end{gathered}`